Define extreme cold...

Airliners operate in very cold conditions while at cruise altitude (as cold as -40C). However when surface conditions are that cold, it can create issues from a systems point of view, but that is more during the preflight period than anything else.

Colder temps will always work in favor of increased aircraft performance since the colder temps lower the density altitude. Other than that, I've never had any issues (in piston GA aircraft or turbojets)... and I have more than my share of cold weather ops after flying in the Dakotas for 4 years.