We were there this year. MLK day itself was MISERABLE. We generally avoid peak times, so it was the worst crowds we'd ever seen. DS actually said he wanted to go home and go back to school, but then, he really hates crowds.
The middle of the week was great crowds-wise, but very, very cold. We were there one day at AK that they didn't let the animals out of their overnight barns because most of the animals need temperate to tropical conditions. We ended the trip with a couple of lovely days, both crowds wise and temperature wise.
Between MLK day being miserable and a couple of the days being miserably cold, DH doesn't really want to go back in January again. I'd been before in January and had lovely weather, so I've convinced him to try it at least one more time before giving up on it entirely.