We were there in January a few years ago. The crowds were low and we had beautiful weather the whole week. However, the week before us and the week after us was rather miserable. It was cold and rainy. I've been to WDW when it was cold and rainy, and I've been there when it was extremely hot. I used to say I'd take the cold over the hot any day, but when it's cold PLUS rainy then you are not only wet, but you're freezing AND wet. When it's hot, you can duck into a building and get some A/C. Or, you can go back to the resort for an afternoon swim. But if it's hot AND crowded, that's the worst time.
LOL...I guess I didn't really answer your question.
I would recommend going in Jan as long as you don't have a baby with you. Trying to keep an infant in a stroller dry and warm is hard.
BTW, we were just there in Sept and I was thinking about going again in Jan...lol. But I think we're going to visit the Dells instead.
Mary