We might want to be clear about one thing.

Butane burns fine in cold weather...it just doesn't vaporize and if it won't vaporize it won't come out of the can in the configuration of the stove in question. Propane has the same issue but the temperature is way colder...like 50 degrees colder.

Addendum:
Butane vaporizes at -1C/31F
IsoButane vaporizes at -11C/12F
Propane vaporizes at -42C/-43F