It should not be too bad as most places (work wise) are open and do not really observe this day. However, any holiday will be busier than a normal day.
We were at UO in 2003 on MLK weekend (and are planning on doing it again, I might add) and the crowds were practically non existant. Of course, the fact that the temperature was in the 30's might have had something to do with that It was a very chilly weekend! But we had a great time nonetheless. We are AP holders and I remember that they had a special promo where AP holders could get up to three express passes at a time; we never needed them. Most rides were walk-on.
oh yes, the 3 Express Passes for AP Holders...haha, that was laughable, wasn't it! But in a good way...not needing them...that's such a good thing! January is one of the favorite times for my family to go. We didn't go during MLK weekend, but that's a big skiing weekend, so maybe people head to the ski slopes instead of the themeparks...who knows? Well, one can hope!