If we return to a more christian origin of Santa Claus, St. Nicholas he would probably be thin. This is from Yahoo
Was the Real Santa Claus Fat?
It was rare for anyone besides nobility to be obese during the time in which St. Nicholas was alive, and bishops rarely indulged in such earthly and gluttenous pleasures. Most depictions of St. Nicholas actually reveal him to be somewhat shockingly thin. This would be consistent with his reputation as a selfless person who gave to those in need, instead of over-indulging in wealth.
http://www.youtube.com/watch?v=WMUWJmV5c90