That was something I hadn't hought about before we went last November...now it is something I am thinking about before we go back this November! It is doable (to wear your coat on the rides) but can be uncomfortable (a bit tight for space with a bulky coat). My son (who was 4 at the time) kept taking his off and handing it to me everytime we went on a ride. It became alot of work, taking off the coat, mittens, scarf and hat...only to put them all back on as we exited...and then off again at the next ride. You WILL need to wear all the cold weather gear, so there is no avoiding it. Bring extra hats and gloves, as you may very well lose them on one of the rides.
Have a great trip! You just can't beat Disney in December...truely magical.