Is Santa a woman.................?

Bilbo thinks so.  You have to admire his logic:

Men can't pack a bag.

Men would rather be dead than caught wearing red velvet.

Men would feel their masculinity is threatened by being seen with all those elves.

Men don't answer their mail.

Men would refuse to allow their physique to be described, even in jest, as anything remotely resembling "a bowlful of jelly."

Men aren't interested in stockings unless a woman is wearing them.

Having to do the "Ho, Ho, Ho" thing would seriously inhibit their ability to pick up women.

Milk and cookies left out by the fireplace? A man would demand beer and beef jerky.

Finally, being responsible for Christmas would require a commitment.