Ill add my 2c here. Although is a smaller rig, I do a lot of winter camping in it.
This is normal to me...
Good tires will make all the difference in the world. Highway ribs will suck ass in snow. As to ski lots, they are the worst, worse than the roads. Always either ice or slick packed snow. They do scrape them every night, but the amount of traffic they see polishes it fast.
Ski in ski out is pretty sweet though...
I would NOT chain up unless you were forced too. There just isnt usually enough clearance. Chains move a lot when your start driving. They will destroy things.
I carry these (maxtrax) they are a god send, on slick stuff it just takes a little traction to get moving. They work great for that.
So my vote is good tires and have fun, take it slow and easy. If your stuck the lot attendants are usually pretty cool and they always have a front loader stashed somewhere to pull people out.