Drywalling in cold weather just has to do with mud not drying. Go ahead and drywall and wait until warmer weather to mud.
How do you know the shared wall isn't already drywalled?And you are using 5/8 fire rock on the walls all the way to the roof on the side that's attached to the house right?
Some areas require you to use 5/8 on the whole gargae since it's attached.
Might want to check into that with the building dept.
If you go to the website I think this is spam. But I'm not really sure.