How do I prevent interior doors from sticking in the winter?
Make your doors smaller .  The jamb stops for doors are usually jutted out a half inch or at the very least 3/8".  There is no need for the door to be rubbing against the jamb that tight to where it would ever stick.  I suggest the use of a small electric hand plane and shave off in 1/32" increments.  You will need to remove the handle and the faceplate.  Also if you get beyond 1/32" you may need to chisel out the faceplate rectangle a bit.    

You can try sanding the area but I have found that by the time I sand, and door works well... I put a few coats of paint on the area and then bam I am back to square one.