It is easy to control the temps in your room if you are onsite so whatever they are used too should be ok. You will most likely need some heat at night in Jan. I would go with long pants and t-shirts, perhaps a new pair of cute disney PJ's!!
For our trip this past January, I went to Target & bought DS7 some new PJs. I got the long pants with short-sleeved tops. Those were perfect. I wouldn't recommend shorts. The evenings/mornings are cold.
I got my girls each 3 pr of the long slv PJ pals from last year and plan on bringing 1 or 2 pr of the short slv ones. as the PP said you can adjust temp in the room and we do like it a little cool to sleep anyway.
My DD wore her summer night gowns and DS wore his boxer shorts. We are from a very cold dry winter climate and the humidity alone kept us in light clothing even though we did keep our room meat locker cold at night.