Another possibility is to remove the door card and the little bit of sound/dust isolation. Just enought that you can see the door handle mechanism. Pull the outside handle to see what and how moves inside the door. Use liquide grass or something similar that is weather resistant. Spray it. As well you can take of the door cables and spray same thing inside. There are humidity and small water drops inside, plus the handles will move much more freely after few days of usage.
Had problems around 0. After few h work it has been good for months(-10 and under).