The Unofficial Guide does say to avoid parks with EMH, but that's really just to say don't go to that park THAT DAY. If you want to get up early and go into the park, the place shouldn't be busy until the park officially opens. At that point, you've already got hundreds of people in the park and you add more.
Same thing with evening hours. Lots of people show up a few hours before the official closing time just to take advantage of the EMH... but if you show up at closing time, it's the coolest thing to stride past all the poor souls having to go home...
We went in January 07, and crowds were pretty light all the time... but they were noticeably higher on EMH days. If you want to avoid crowds, don't spend the day at the EMH park.
As far as rain, well, there are two things to consider: First, all rides and shows should be functioning, except EE, which would only close due to lightning. Secondly, the animals should be out unless it's deemed cold enough to be dangerous. If so, they might be brought inside... I think AK (or any park, for that matter) would be fine in the rain.
Buy ponchos at Wal-Mart before you go. And bring more than one apiece. I ended up giving mine to a girl in a wheelchair at MK and had to buy a premium-priced Mickey poncho (but I did get tons of brownie points from my DFi for my generosity!).