We (inadvertently) went to WDW during MLK weekend this year. We didn't realize it until all of the plans were made/reserved. The only thing we changed upon realizing it, was we made our day "off" on that Monday (the actual holiday). We did AK all day Saturday until closing and then popped over to MK for Spectro and Wishes and SeaWorld Sunday with no problem and manageable crowds. We spent Monday at DTD and at the hotel. Tuesday thru Friday was quite manageable. A bit more crowded than our previous January trip, but really no problem. We used FP as often as we needed. DD rode RNR in MGM eight times in one day! So obviously the crowds were VERY manageable!
We discovered that there were several soccer tournaments in town over the weekend and that most of them ended Sunday and the families would head to the parks on Monday. So I am glad that we avoided the parks that day.
About the weather..... 01/2002 we had one day of rain, but it did rain light to heavy almost all day that day. 01/2004 we had a morning of rain (heavy) that became a beautiful afternoon and an overcast morning that turned into a rainy/cool afternoon. In addition to that we had one other day that was very cool (and we are from NH!). We spent our Epcot day bordering on uncomfortable. We all wore shorts and sweatshirts, thinking we would take the sweatshirts off when it warmed up.... IT NEVER WARMED UP! We ended up leaving about 6pm (before Illuminations) because we were all too cold. The vendors were selling blankets, hats, and mittens! We learned our lesson and packed a bag with warmer clothes and long pants the next day and put it all in a locker. Right before Fantasmic we changed into our warmer clothes and were all set for the show!! But that said, most of our days were shorts/t-shirt weather for the afternoons. Mornings and late evenings were cooler, requiring at least a sweatshirt, sometimes long pants.
ANYHOW... sorry to drag on..... just be prepared to dress in layers and possibly have warmer/dryer clothes nearby just in case. If we had done this our day in Epcot we would have been able to stay for Illuminations...oh well.
Hope this helps...................P