Can you remove the shafts and store them indoors? May be too much trouble for some implements but would cut down on the amount of rust.
Sorry about the grease recommendations, I live in Texas and don’t consider what cold temperatures can do. I think that something like white lithium grease is good for cold but I don’t really know much about it. You might stop by a snow mobile shop and ask them what they recommend.
Since you mentioned that you have shaft’s without covers you can get the safety shields from
Bare-co.com
I have one and it is easy to get the shield loose to slide back out of the way to connect the shaft to the tractor and then reattach it when connected. It has some levers that pull up by hand instead of having to use some tool. But you would probably have gloves on and need a small pry bar to use.