We went in January of this year....the 18-22 to be exact. I think that Monday was a holiday. It tended to be a little bit busier, I think, because of that. However, the lines were not that long. According to several sources, it is one of the least crowded times to go.
As for the weather, we had some of those crazy storms blowing in at that time. Normally, I don't think it's like that. It was a little on the chilly side (coming from a Texan) but one afternoon we were wishing we were in shorts. Of course we went back to the resort to change before dinner and a cold front, complete with lots of cold rain, blew in while we were eating. But, as I said, I think this was not the norm. DBIL is from Daytona and visited WDW a lot growing up. He said January is one of the best times to go and the weather isn't all that bad. There were even people swimming.
As for taking the kids out of school....for 3rd grade, I say go for it. Make sure there aren't any state mandated tests for that time (the school district should already know). Sooooo many people do it. And I even heard people talking about it while we were there. I haven't done it yet, but I have one in high school which is a little trickier.
Good luck!!