I have read many posts about using a spiked gauntlet(s) with a pole arm to threaten adjacent squares. My question is, would I still be able to threaten adjacent squares as an archer who uses a bow?
Yes, you can, if that hand is free.
Releasing your grip off a weapon is a Free Action, according to this FAQ item:
Two-Handed Weapons: What kind of action is it to remove your hand from a two-handed weapon or re-grab it with both hands?
Both are free actions. For example, a wizard wielding a quarterstaff can let go of the weapon with one hand as a free action, cast a spell as a standard action, and grasp the weapon again with that hand as a free action; this means the wizard is still able to make attacks of opportunity with the weapon (which requires using two hands).
As with any free action, the GM may decide a reasonable limit to how many times per round you can release and re-grasp the weapon (one release and re-grasp per round is fair).
And this is exactly the tactic used with two-handed weapons and spiked gauntlets, so you can threaten adjacent squares instead of threatening two squares away and have all adjacent squares as dead zones, while it is not your turn.
Releasing your off-hand from your two-handed weapon (be it a spear or a bow) will allow you to use that hand for attacks of opportunity with the weapon on that hand (say, a spiked gauntlet). This is no different from attacking with a bow normally for a round, then using Quick Draw to grab a dagger and be armed until your next turn.
However, if you are using your two-handed weapon, you cannot use your off-hand weapon (a gauntlet) on attacks of opportunity before first spending a free action to release it. Like when using the Greater Trip feat using a two-handed weapon, tripping your opponent, then attempt to use an off-hand weapon to deliver the attack of opportunity.
So, the tactic usually goes like this:
- Make your attacks with your two-handed weapon.
- Release your off-hand as a free action before the end of your turn.
- Threaten adjacent squares while it's not your turn.
- Grab your weapon again at the start of your turn.
But honestly, this is no different from using your bow as an improvised blunt weapon while it's not your turn, as long as you also spend a free action changing your grip.
When asked if you can attack with a spiked gauntlet while also attacking with a one-handed weapon on the same hand, James Jacobs (Paizo's Creative Director) answered this:
You can't because you're using the hand with the spiked gauntlet to attack with the sword. If you want to make a spiked gauntlet attack as a secondary attack... put it on the other hand.
If you want to attack with that spiked gauntlet while you're holding a sword INSTEAD of attacking with the sword... I would charge you a –2 penalty on the attack roll due to the awkwardness of having that hand full at the time. I might even rule you can't attack; you'd have to switch that sword to the other hand (which is a free action so why not?) before you attack.
What about the controversial FAQ about using off-hand attacks on the same turn as attacking with a two-handed weapon?
This FAQ Item caused a lot of confusion when it says:
Armor Spikes: Can I use two-weapon fighting to make an "off-hand" attack with my armor spikes in the same round I use a two-handed weapon?
Likewise, you couldn't use an armored gauntlet to do so, as you are using both of your hands to wield your two-handed weapon, therefore your off-hand is unavailable to make any attacks.
Here it says you cannot make off-hand attacks while attacking with a two-handed weapon on the same round, which leads to many other FAQs (like the ones I mentioned previously) to be wrong. The confusion caused by it can be seen on several threads at paizo.com (#1, #2, #3, etc).
But to put it simply, that FAQ would lead to many situations where you could not use any hand that already made an attack on that round, which is not what the rules actually say, as you can obtain several attacks with the same hand (like iteratives).
That FAQ was addressing a specific situation, attempting to use an off-hand weapon (spikes) to two-weapon fight while already using a two-handed weapon, and shouldn't be considered outside of that scenario or the entire combat chapter falls apart.
An alternative to avoid all this confusion is wearing a Dwarven Boulder Helmet, which allows an extra attack with your head and not your hands, and it makes no mention of working as an off-hand attack, unlike spiked gauntlets or armor spikes.