It's not from cold. It's from the lock mechanism getting gummy. It's just exacerbated by cold partly because it makes the grease gummy but compounded by mental conditioning that we in colder climates will assume the door deal is frozen and pull harder. The hard rug will break the axle through the hinge.

I posted photos of a relatively easy fix using 16ga steel wire. If I have to do again I will use a steel band strap (looks like cable tie but stainless steel vs nylon).

I have a broken one that is be willing to fix and send on to somebody needing a driver door carrier. I only paid $35-40 for the knock off copy I used to fix wife's car but I moved over the cables from the oem they were much better made.

I repaired my wife's broken carrier and used in my car (swapping the BMW cables). I also greased up the gear part and used it only some dry lube on the trouble part so it won't gum up in winter.