You should be OK. Out of all my trips to WDW, at least 60% of them have been the last week of February into the first week of March. I found it to be an ideal time to go. There are additional people in the parks during that time mostly because the way up north frozen people get to go because they have a mid-winter vacation in the schools.
I found it to be pleasant crowd wise. Just enough to make the place seem alive and jumpin', but, not enough to be stepping all over people. I have seen some tour groups, but, not very many. Most of the attractions are open because spring break folks start to show up the following weeks. The weather has always been good when I was there. Cool in the morning, but, quickly warmed up. I, being one of those frozen northern people for many years, was quite happy and comfortable wearing shorts and T's. I can specifically remember having the car heater on in the morning and by noon running the AC. The kids always used the pools. I remember only one day that was chilly all day long in all of the trips. In all those trips I was rained on only once and that was a surprise. It happened after dark and came in totally unexpected and unseen. It was, however, a truly Florida type rain experience. Rain coming in sideways and in buckets. There was no need to run because after about one minute you just weren't going to get any wetter. That can happen anytime of the year in Florida.
When I can work it out, it still is my preferred time to visit and I no longer have any kids in school. I do have some grandkids in school, but, I currently live in North Carolina and am not anywhere near as frozen as I once was and they don't get that same school break. They are weak down here. If they get so much as 4 snow flakes the schools (and everything else for that matter) close down for a week anyway. So, they are always having to make up snow days.