Does the game differentiate between an arrow aimed at an enemy's head and one aimed at a limb resulting in a difference in damage?

No. One of the devs posted in a thread yesterday saying that headshots do no more damage than body shots.

Nope. Headshots are still amazingly satisfying though.

No which is very annoying when you are playing as an archer.

I don't know how hard this would be to mod in though?

Sadly no, but modders did mod it into Oblivion so there may be hope for a mod that does this in Skyrim.

No matter what, like another poster mentioned, it's still extremely gratifying to walk up to a newly perished bandit to see two arrows sticking out of his forehead a la Robinhood style.