We've been in the beginning of Jan - the weather was sunny and cool - I believe the mornings were in the 50's - the highs were in the 70's - but I do remember taking my sweatshirt off and feeling warm in the afternoons! Never had a drop of rain! No wind - it was beautiful, as long as you bring a light jacket or sweatshirt for the mornings and evenings. It never was warm enough for me to go swimming - but I am a bit of a wimp.... The crowds were non-existant. We pretty much walked on rides. However - with the 50th going on - who knows!!! Have fun!
I agree with AFMom. Although it is the beginning of rainy season. My DD18 had her birthday party many times at DL (Jan 11th) and a few times it was rainy. But, the crowds are very low and it never really gets that cold here by east coast standards If you can swing it, I would do it, we have been hearing every month about huge crowds due to the 50th and typically Jan and Sept are the slowest months. Good luck deciding.