Others have noted this before:
In some systems it is easier to integrate hidden roles than in others.
Also: Players tend to have different opinions on the matter and you have to find a compromise that works for the whole group.
If you cannot find a consensus right away, you might want to try different amounts or criteria for hidden rolls in different sessions and then discuss with a common background.
It is OK (recommended) if your players are alright with the general idea.
A few more additions:
Never let any secret roll affect the flow of the game (dialogue, description etc.).
If there are passive rolls like luck, sense danger, sense motive, etc., some of which can be used by explicitly concentrating on them, in some sense they are always on, even if the character does not actively try to use them: keep notes on the characters' values. It can pay to always roll certain unintentional checks in secret and only let them influence your descriptions, so that the players never know whether you rolled for them or for something unrelated (does the monster notice the loose boulder above it?).
When rolling in secret and the roll is a critical failure, no-one saw it and could complain about you handling it like a normal failure. Done right, this kind of cheating can enhance the fun for the whole group. It is also important that you never let them deduce from your descriptions what you rolled for and whether it was a success or not.
When rolling for enemies, I always roll in secret. As well as keeping the initiative list secret — this can make fights a lot more interesting. Also, so that players may not know how many enemies there are (some could still be hidden but may need to roll to prepare some spell), you can take different coloured dice for each enemy and roll all at once.
I also tend to always play around with my dice, so players can never be sure whether I actually rolled them for a check. With some practice, they will even have problems determining whether you looked at the result or not.
If you know your situation and your characters well, you will be able to roll in advance, such that the result will affect your descriptions several minutes after the roll … by then there might have been other rolls to obfuscate what you were rolling for.
An important aspect (IMHO) is that, even if the players are in full control of their characters, there can always be situations in which following a complicated chain of dependent rolls would disturb the gameplay… a very bad example: the character steps on an unusual rock and this needs a roll for some sense or other to determine whether the character felt that through his thick shoe and if that is the case, other senses have to be rolled for to determine whether the character notices that something is off.
Now, if you let the player roll all of that, you won't get past the first roll before the whole group jumps into action — whether that roll failed or not.
You could just decide whether the character feels something through his thick shoe or not. But if players want to be in control so badly that they do not want you to make hidden rolls, just deciding something will cause problems as well.
If you do all rolls hidden except the one that lets the character spot that something is off, the situation feels entirely different. If the player's roll succeeds and the character thinks about why he feels that way, you can always make your previous rolls public.
This has a lot to do with how much control the GM has over the storytelling part. This is partially regulated by the game mechanics and the rest is again the social contract of the group.
And the group has to decide how much control they want and how much suspense they want etc. So if the players want, for example, to be able to feel the horror, tension or confusion of their characters, it can be helpful to not always know all variables. Also, not knowing why you feel a certain way, or whether that shot was a good one, is a sort of suspense.
Some claim that avoiding to roll in secret for the players makes the game more realistic. I tend to disagree.