I always keep clear plastic 30 gallon bags in the pouch of the seat. When it rains, I put one over the tiller (handlebar area). The battery is sealed, so you shouldn't have to worry. Avoid deep puddles.
I also keep a rain poncho with me. I put it on me & drape it over the back of the seat. It keeps the seat area dry as well as keeping me dry.
If you should stall out - you can put it in free wheel mode (handle is near battery pack) & push it to a dry place (like one of the stores).
Summary - plastic poncho & plastic 30 gallon bag
Enjoy your time at Disney!