As long as you have the motor tilted all the way down, so the water runs out (keeps freezing water from ruining the motor) there should not be any problems. If the batteries are left out they may go dead, but you can always bring them in or get a full charge on them before you leave the boat. Of course running will not hurt a thing as long as you have some water running to the water pump so your impeller doesn't get burnt up.
I leave mine under a open shelter year around and I have never had a problem... the only thing I do is put the full charge on, drain the water and leave it for the next trip.
Usually I fish in the winter some too, so it don't sit all season.
I noticed your in Bama so the weather should be pretty moderate like here in NC...
Good luck...Happy Fish'n