Yeah...but an stuck solenoid would kill off his battery super-fast (winch at stall load) and cook the motor pretty fast too...and (as much as I hate to say it) I think that Trev is right - an solenoid stuck in the open position will not allow current to flow. I think your solenoid stuck closed, buddy.
This sounds like a relatively slow drain, located within the winch or it's wiring.
One question for ya Marco...does the winch work?