I don't correlate Santa with religion either, unless you are looking at Santa as a St. Nicholas figure. I get what you mean. At a Catholic school, Jesus certainly is the reason for the season.
It's funny. Since we do holidays and celebrations in Grade 2 here, this week we are learning about Christmas. When we got to "Who celebrates Christmas" the answer was Canadian Christians (because we look at things from a Canadian perspective). The number of kids in my class who were adamant that they weren't Christian but still celebrated Christmas surprised me. I was thinking to myself, "Me too!" but of course also needed to explain the Christian roots behind the celebration.