Yes, you can.
HOWEVER -- At the very least you need something like a shower cap to put over the control box. The motor assemply is sealed and so should not have any problems with puddles but don't try to ford any streams.
What I will do is wear a poncho, flipping the back behind the seat and using the front to make kind of a tent. Usually in warm weather I am wearing shorts and sandals, so if the bottom of my legs and my feet get wet it is not a real problem at all.