Hi Stephanie:
My kids are now school-aged and vacation for me now is dictated by the school calendar, but before I had kids, my favorite time to visit Walt Disney World was in January. In general, crowds at Disney World tend to be smaller when schools are in session. Since January tends not to have many school breaks and offers cooler weather than the summer, January was always my preferred time to visit. February and even early March should also offer you similar crowd and weather benefits. Because schools tend to offer spring breaks on a rolling-basis between mid-March through April, crowds tend to pick up during those weeks.
The weather in Orlando in January usually hovers around 70 degrees fahrenheit. However, during certain cold snaps, the weather can really dip low, to the 40's or even lower. I was at Disney World two years ago during the first week of January when it was unseasonably cold. However, when I was at Disney World three years ago in early January, the weather was in the normal 60s and 70s. So it's always a good idea to dress in layers in case the weather changes unexpectedly. The good news is that Disney's Resort and Water Park pools are heated all year long.
Note that Martin Luther King Jr. Holiday falls in January, and crowds tend to increase slightly during days surrounding the Holiday.
Walt Disney World Marathon Weekend also falls in January, bringing in runners, friends and family. However, even with these two January events, I've found that crowds in January are very manageable compared to many other times of the year. Plus, if your vacation dates are flexible, you can likely plan around those weekends.
Enjoy your winter vacation.