In most of what I have read it is best to always keep the drive lowered/down. Logic and reasoning is that it keeps stress off the bellows, therefore getting longer life out of them. Plus drains the water out. Mine is in the garage and in the desert we get maybe one or two 32 degree nights.
You need to lower the unit so that rain water does`nt fill the prop/hub area and freeze and crack the housing. Plus giving the bellows a break like Palace said.
As everybody else has said it's real important to keep the drive in the down position so water doesn't get anywhere in the casing and freeze and crack anything. Also when the drive is in the up position the Bellows is stretched out. If you have a real cold winter it can contract and pull itself off or crack. I may be overly cautious but I remove my drives for the winter. 1) less chance of theft. 2) less chance of any water intrusion and 3) Gives me a chance to inspect the internals before using the boat for another season.
I have twin i/o's and have been dry docked so dang long i placed 2 small jacks under the skegs and jacked em up a tiny bit to relieve the downward stress on the transom. They are still in the down position and i imagine you have to be careful doing this so you dont cause stress in the other direction. Just a comment about what i am trying for long term. Jeez going on 3 years now in dry dock. The new trailer tires i bought when i picked this up are starting to dry rot. I keep them covered too.