In my opinion, it is appropriate, but I would get one card and sign it together with your peers.
Others have pointed out that it's culturally dependent. That's surely true. In some countries one will see nativity scenes throughout towns and villages. Personally, I think all other public decorations I remember seeing are pagan, and I'd speculate pagan celebrations ("Christmas" trees, Santa Claus/Father Christmas, lights, etc.) should rather offend Christians than irreligious people.
However, there might be an issue if the lecturer always gets cards from some people but not from others. Therefore, I would recommend to get one card together with your peers, and all sign it together. That mostly eliminates the problem of favouritism.
(Personally, I would not be offended at all by receiving a religious Christmas card at Christmas, a Jewish card at Hanukkah, an Islamic card at Eid, etc. It would make a delightful collection above my desk!)