Note: I know that Gygax recommends at points keeping almost everything a secret from the player (including, if I remember correctly, a player's character's hit points), but I don't know if this exactly is a thing, and I still find previous editions' combat mechanics largely opaque. By way of background, I'm considering updating several classic adventure modules for an upcoming dnd-3.5e campaign because, although many of the players have heard of or even read some of the adventure modules, none have played them. The dnd-3.5e Player's Handbook says that "each combatant makes an initiative check" (136), but I was considering trying to maintain an old-school feel. If initiative results were kept secret in these previous editions (from which most of the adventure modules come), a house rule about secret initiative would be a relatively simple yet still significant step toward achieving that feel.
Answering the simple question: neither mandates hidden rolls, nor the DM rolling initiative for the players' characters. DM initiative rolls in AD&D are (usually) open, and in AD&D 2nd Edition can be either but it's usually a moot point.
Let's look at that in detail.
AD&D and AD&D 2nd Edition have subtly different combat and initiative procedures, and these impact the context of open or secret information. Both are different in significant ways from D&D 3.x combat procedures, significantly impacting what information is useful, and how and when it is. So for each, we're going to look at how combat works overall, to put initiative determination and knowledge in its functional context. This will show the significance (or lack thereof!) of hidden or known enemy initiative rolls.
AD&D's combat context: Who has the initiative is an inherently known quantity
In AD&D, combat is defined in the DMG because the combat procedure is DM-handled, not player-facing. (However, much of it is procedurally exposed by the DM in the normal course of a round.) Initiative is per-round, but each of the (usually) two sides in a combat share initiative. There is no personal speed adjustments, because (ibid)…
Because of the relatively long period of time represented by the round, dexterity (dexterity, agility, speed, quickness) is represented by a more favorable armor class rating rather than as a factor in which opponent strikes the first blow. Likewise, weapon length and relative speed factors are not usually a consideration.
This matters because it reduces the possible permutations of known and unknown information.
Furthermore, AD&D combat has the side with the initiative both declare and resolve all their actions before the other has a chance to declare or resolve their actions (DMG, p. 61, encounter and combat steps 4 and 5).
As a consequence of per-round, per-side initiative and full declaration and resolution of actions of one side before the other, who has the initiative is is effectively immediately revealed regardless of whether initiative is determined with an open rolls or a hidden DM's roll. There is no point at which the PCs are required to make decisions without knowing whether they or the enemy will act first.
AD&D rolls are usually made in the open
For completeness though — and to fully understand why initiative is not only a mechanically-known quantity, but is intended to be so because it is fictionally-known too — it's worth seeing how it's generated.
The authoritative statement on initiative procedure is in the DMG on page 62:
It is recommended that such initiative rolls be made openly unless there is some reason to hide that of the encountered monster party bonuses which would be unknown to the player characters involved.
Notice the bit about modifiers unknown to the PCs being the relevant point of decision: it's saying to make the roll in the open normally, simply because the PCs would (on the 1-minute scale of AD&D combat) have ready access to initiative information simply through their own senses. In much of AD&D's writing about combat, the term “the initiative” is not representing an abstraction — it is representing literally who has the initiative (“the power or opportunity to do something before others do”). In combat, who has seized the initiative and holds it over the course of an entire minute (an agony of time in mortal situations) is readily apparent.
The exception is only made to maintain AD&D's default secrecy of monster statistics. Yes, this gives away that there is something unusual at play, but it doesn't hide who has the initiative (and AD&D is okay with clever players deducing monster statistics from the information they've gathered through direct experience fighting them).
AD&D 2nd Edition's context: Who has initiative is inherently unknown
AD&D's initiative-determination procedure doesn't mandate either hidden or open rolls, but it doesn't need to — by the time initiative is rolled, the information is moot because of the combat procedure 2e uses.
Specifically, each side and character must decide their general plan of action before initiative is rolled (PHB, p. 93, The Combat Sequence, steps 1 and 2). Combat is also per-round. Combined, these make initiative an unknown quantity every round.
This makes the decision-making value of initiative information mostly null by the time it is actually rolled. It's not entirely null though, because within the general plan of action, each character can determine the details on that plan when their turn arrives, and because the DM can (at their discretion) make allowances for reasonable changes to plans based on significant changes to the situation (ibid, emphasis mine):
[T]he players give a general indication of what their characters are planning to do. This does not have to be perfectly precise and can be changed somewhat, if the DM decides circumstances warrant.
That is immediately followed by an example that clarifies what “in general” and “not perfectly precise” is intended to mean:
If the characters are battling goblins, a player can say, “My fighter will attack” without having to announce which goblin he will strike. If the characters are battling a mixed group of goblins and ogres, the player has to state whether his character is attacking goblins or ogres.
In practice, what this worked out to with my groups was that actions that became invalid (e.g., the declaration was “I want to heal the fighter”, but now the fighter is no longer within movement range due to an unforeseen tumble down a hill), could be altered. Usually this didn't seem to confer much advantage (because the available options weren't one's first choice), and it didn't come up often enough to slow down combat notably.
AD&D 2nd Edition initiative rolls being open or hidden is moot
Because you have only limited ability to reasonably adjust (or more rarely, entirely change) your plan, by the time you are actually taking your turn there is only a little difference between hidden or open initiative rolls: by then, you already know who has gone and who hasn't. This is especially true when using the default per-side initiative rule, even if using personal modifiers to that one roll: once the rounds starts, it's obvious who goes when.
Even using individual initiative (which is, again, not the default, so adventures don't assume it either), there are only rare situations where your flexibility on your turn lines up precisely with opportunities created by initiative differences. Rarely is the normal choice of attacking Ogre #1 or Ogre #2 different, and when it is, rarely enough to be much real advantage. Hidden vs. open initiative might help if your action is entirely invalidated and you get to make a (reasonable) whole new plan (with permission), but invalidation isn't under your control and happens rarely enough. So hidden versus open initiative only matters very rarely, and only when using an optional initiative rule.
The sum result being that, in 2e, initiative is unknown, but the kind of flexible group coordination allowed by D&D 3.x's information situation during combat is not dissimilar to what 2e permits under its default per-side initiative rules with up-front plans for each side. In 2e it's just as possible to (try to) make “optimal rounds” happen — you don't even have to worry about carefully executing each PC's turn correctly, since a side coordinates its actions during its turn.
Conclusion: You can just use 3.x combat unaltered
There is not going to be much impact on combat encounters if you use 3.x initiative and combat procedures unaltered. There is enough chaos and lack of 3.x's levels of balance-concerns built into AD&D combat encounters, of either edition, that the minor advantage of being able to decide a PC's actions completely on their turn will mostly be washed away by the more-significant noise caused by the conversion itself and the different balance paradigms, and perhaps be counter-balanced by the higher effort required to coordinate the PCs' actions in 3.x.
However, if you want to import a characteristic bit of AD&D combat's feel, and maybe even enjoy some of the speed and coordination effects the AD&Ds expect from combats, you may wish to experiment with adding a “declare general intentions” step at the top of every round. (For the DM, this would be a “secretly decide general intentions” step, instead.) Even without making such declarations at all binding, you might find that priming each player's thoughts speeds up turn-taking and aids coordination.
(If you have a group that engages in round-planning optimisation already, this might seem like it makes the game slower, but that's because they're only doing it for already-complicated rounds. If they tried such a complex round without planning, you'll notice it's even slower! Pre-planning speeds up simple rounds too, and the planning overhead scales down with simpler rounds as well.)
I don't know the answer for AD&D2e, but the 1e DMG, p62, says:
Surprise gives initiative to the non- or less-surprised party. It is otherwise determined when an encounter occurs and at the start of each combat round. It indicates which of the two parties will act/react. Again, a d6 is rolled, and the scores for the two parties are compared. (It is recommended that such initiative rolls be made openly unless there is some reason to hide that of the encountered monster party — such as special bonuses which would be unknown to the player characters involved.) The higher of the two rolls is said to possess the initiative for that melee round.
So Gygax is saying that initiative should be rolled openly unless there's good reason otherwise, but in any case, as the round starts it seems to be knowable by the PCs which side actually has the initiative. Not letting the players know who has initiative deprives them of a lot of their ability to use tactics and generally play combats, as opposed to have a DM narrate them.