go to weather.com and look at March & October averages to get a better idea of the weather during your specific planned travel time. We usually go in October and the weather varies somewhat from the start of the month to the end. Some years you run into the tail-end of hurrican season at the beginning of Oct., so may have rainier weather. The end of the month is generally one of the drier times in Central FL. We just came back from an early March trip and we had 2 days of 80's, humid, scattered thundershowers, and 3 days of 60's, so weatherwise I'd say it's a crapshoot (just like Chicago!)
We prefer Oct. for the smaller crowds, but we love heat & humidity, so the Oct. weather doesn't bother us. We must have hit the parks a little differently than bailey405, as we thought the crowds on the 8-10 were pretty bad. We fast-passed a lot to avoid 40-60 minute waits for Splash Mountain, Big Thunder, Kilimanjaro Safaris, etc. It was manageable, but we didn't need to cover a lot of ground.
We did take my aunts, 84 & 81 at the time, in Oct. one year, and we lucked into great weather up until the last day. Temps were in the low 80's, but the humidity was relatively low.
Now that I've probably confused you more, definitely look at some weather averages/historical highs & lows at weather.com.