Hi, BarbB. A friend and I spent MLK weekend (Thurs.-Mon.) at WDW this year. Most of my trips to WDW over the years have been over Easter week and once over Christmas week. Let me tell you, there is NO comparison!! I found MLK weekend to have far smaller crowds than those holiday weeks. No doubt larger crowds than the rest of January, but I have no point of comparison there.
For most rides or attractions, we had a wait time of 15 min. or less. We did use fast pass for Test Track, RnR, and a couple other things. The busiest place we came across by far was Magic Kingdom on Saturday afternoon and evening. That was the only showing of Spectromagic for that week, so I'm sure that probably contributed to the very large crowds in MK that day.
One factor may have affected the size of the crowds in general that weekend. It was really cold!! It was warm and gorgeous when we arrived on Thursday, but a cold front came through that night. For the rest of the weekend, temps stayed in the 40s and low 50s though at least it was generally sunny. Naturally, when we left on Monday, warm weather was starting to return.

But we figured that the cold snap might have discouraged some of the locals from coming to WDW that weekend.
Our strategy was to make full use of early entry days. That worked well for us. By the time the early entry park was starting to get busier (around midday), we would catch lunch somewhere. We usually took an hour or two to put our feet up back at the resort (BCV), and then hit a different park for afternoon & evening. The parks close earlier, of course, than over the holiday weeks when I usually go. But that was no problem, because we didn't have a lot of wait time for rides. It was actually nice to be back in the room by 10:00 or so, and get a good night's sleep since we were doing early entry.
Hope that helps. I'm not an expert on MLK weekend, since I've only gone once at that time. But that was our experience. We had an awesome time in spite of the cold weather. Good luck as you plan your trip!
