Is it just rechargeables (Nicd and NiMH) that aren't supposed to like cold temperatures?
We have a WH1090 weather station in the garden, powered by two AA alkalines ( Costco /Kirklands ie nothing special) , and it worked fine at the lowest we've seen so far; -11.4C.
According to the specs it can go down to -40 but I don't think any batteries would like that.