Living in Montana I have to put up with winter or cold weather for about 9 months of the year -- and the other 3 months relatives visit!
I've learned to be real careful about getting involved in outdoor gigs in early spring and late fall.

I don't have any special outdoor instruments, but leaving a guitar, or banjo or fiddle in their closed cases until they have time to get used to the ambient temperature is an extremely good idea. Years ago I threw a little classic guitar in the trunk of my old car, with no case (I was poor, and ignorant), drove 30 miles on a 20-below night, and hauled it in to play at a nice warm houseparty. I couldn't figure out where all the jillions of cracks in the finish came from next morning!

I've found that the cold generally affects my fingers before it affects my banjo. Below about 50 degrees they just won't roll. I think that fiddlers may be able to handle temps below that. I remember one gig we did for a trail ride group up in the mountains. The evening temperture really dropped, and we were playing around a roaring camp fire. If you stood facing the fire, your face and fingers roasted and your backside froze. Every so often I'd turn around and play outwards; then my banjo head would change tension and my fingers wouldn't roll - it was so miserable I finally quit playing. But the fiddles (and fiddlers) didn't seem affected. The guitars seemed somewhere in between. Cold is no fun.