Can a Zen Archer Monk making a full attack with a longbow react to subsequent ranged attack against him with deflect or snatch arrows? Or does the full attack require both hands during his entire turn?
You need both hands to use a bow, but only during your turn. During enemy turn, you can hold it in one hand and have a free hand to use Snatch Arrows.
It also works when you use a two-handed melee weapon and release your grip on one hand at the end of your turn as a free action (but you won't be able to use your weapon for attacks of opportunity in this case).
From the combat rules FAQ :
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).
No matter how you choose to interpret it, you always have a solution to have a free hand during enemy turn.