I live on the west coast of FL about an hour from WDW. Yes, winter is not typical of rain here but it does rain through the winter. March/April are actually the driest months.
Nights are cool (cold to us who live here) but day time highs are definately t-shirts/shorts. I'd bring layers. And even though it's scheduled to rain here
(60% chance near St. Petersburg), That 60% is highly unlikely to be an all day event.
I've read on the boards that many people go to their local dollar store to get rain ponchos to bring rather than buy them in the world. Living in FL, you kind of learn to duck in some where and hang out for a while and then the rain. You still should have good weather.