It's completely acceptable to leave your grill outdoors during the winter. It's even more acceptable to cook on it too ;-)
Preparing Your Grill For Winter:
It's completely acceptable to leave your grill outdoors during the winter. Just clean it up really good by making sure the exterior and grates are all free of grease and debris.
You can easily find some excellent covers that are sturdy enough for leaving the grill outdoors. Make sure you buy one that fits your grill perfectly, and you shouldn't have any problems come spring.