Hi BigLes,
It sounds to me like you're problem is more underground moisture rather than condensation.
I think shutting the cover on it and keeping it down there would be my choice.
If you vent it you could end up just worrying about your cars and tools everyday.
Winter doesn't last too long, sit it out and then consider lining it later. Maybe even just lining it with fibreglass matting.
Good luck
| 
