We were there this past March (the first week) and the crowds weren't too bad (we arrived early). The weather was beautiful. Some days it was a bit warm for me (not humid, just a hot sun), but I'm not a fan of the heat so most people would probably be fine. My boys swam in the resort pool.
I know that when planning the trip, we checked crowd numbers and we felt that the first week would be ok because it was before most people arrived for spring breaks and such.
I think if you go 2 weeks before Easter you'd probably be ok.
With that said, we're planning a trip for January 2008. I'd love to go back the same week in March, but we were homeschooling before and school schedules didn't matter. This year both of our older boys are going to public school and we don't want to take them out for a whole week. So we've chosen a week in January when they'll have Martin Luther off as well as 2 days at the end of that week. I'm looking forward to it. I think the weather will be cool (Fall is my favorite time of year and I think the weather will be similar to that) and the crowds low (except for MLK). I'd much rather walk around with a sweater on and not get tired from walking in the heat. From what I've looked at, the average temp. in January is 60-70 (the high of course). I know people have said it can be colder or hotter, but those are the averages. I checked out the temps for those dates and the last two years and it looked good. I'm keeping my fingers crossed!
If you have any questions about the beginning of March, let me know!