I think I'll always vote in favor of going in January. We went the 2nd week last year and I had a fantastic time. The crowds were perfect; plenty enough to make you feel like you were in a fun place sharing the magic with lots of others, but short and reasonable waits for almost all the attractions. Between the lighter loads and fastpasses, even for the most popular attractions we waited 15 minutes at most (the only exception was when we went on Soarin’ late in the day once, and had to wait about 25 minutes with fastpasses).
The weather was pretty close to perfect. No rain, pleasant temps the whole time around the low 70’s. It did get a little chilly at night, so I’d bring a sweatshirt, jacket, or hoodie! I think the unpredictable temps could definitely be an issue for some people, but it was steady for us. Plus, coming from frozen Illinois, we were happy with any sunshine!
The week we were there was, according to most guidebooks, statistically the lightest week of the year. This was great for us because the resort rates were low and affordable. We stayed at Pop Century and had no problem getting to the parks from there, usually waiting at most 5 minutes for the bus. Getting back from the parks at the end of the day took longer though, sometimes we’d have to wait 20 minutes or so if the bus filled up. At the end of the week things got a little heavier that Friday, both because of the long weekend and also because there were a couple youth programs/conventions that seemed to be visiting, but it was still very easy to get around.
There are a few downsides to keep in mind though, just so you’re prepared. Because of the cooler weather, Disney shut one of the two water parks down for refurbishment during our visit. The other was still open, but it was still too cool for us to take advantage anyway so if water parks are your thing, I'd wait until later. Also, a couple of premiere attractions were also closed for refurbishment as well, notably the Rock n’ Rollercoaster and Splash Mountain (we guessed that Disney liked to use the lighter crowded times to repair some of their more popular rides). Finally, the park hours were shorter but with how easy it was to go on the rides, this actually worked out great because we still saw everything we wanted and then got back early enough for a shower and good night’s sleep.
All in all, I’d definitely go again during that time if I could. It was the first Disney trip I planned and booked/bought for myself, and the light load in the park made it great because we didn’t have to stick to this super-rigid plan or timeframe to see all the stuff we wanted to. We had the freedom to do whatever we wanted as it occurred to us, and it let us just wander around the parks at a relaxed pace and still do more than we could have had we gone in the summer.