R’ Elyashiv says that the reason is that on Dec. 25, all the christians go to pray and there is so much tumah in the world, that al pi kabala if kedushas hatorah comes it can be extremely harmful.
Based on this reasoning, it should be a greater problem to learn on Easter. Church attendance is much greater on Easter. In addition, Easter is far more of a holy day for Christians than Christmas is.
The Wolf