To answer both questions, being a Muslim, there is very little I do about Christmas. Though Islam recognizes the significance of Jesus Christ as the Messiah, and the one who will save us, we do not celebrate Christmas in any way, shape or form. We don't get into the shopping frenzy, we don't put up a tree, we don't invite people over... we just enjoy the holiday away from work, or school.
On a personal level, I have no problem participating in Secret Santa or any other gift exchange through work, because I think it's nice to participate in such programs that warm up the office, and let you build a tad bit warmer relationships with your co-worker(s). Also on a personal level, I've debated whether I should buy gifts for my friends who do celebrate the holiday. I've wrestled with the idea for years, and still don't know what my feeling is on the subject. I try my best to wish everyone happy holidays, and have even given cards in the past, but there is still the question of gifts. This year, I am spending Christmas day with a friend, and so, I actually want to give a gift.
In conclusion, it's safe to say that I basically just hang out at home, and enjoy the time away from work, or school... or as I'm doing this year, I spend it with friends.
Merry Christmas to all who celebrate it, and Happy Holidays to everyone else!