It is -31 degrees Celsius out there and my garage door opens only about two feet and closes down again, each additional time I try it opens even less. How can I get it to open all the way? Should I leave it a little bit open when I know it is going to get so cold?
Thanks!

Don't leave the garage door partly open whatever you do as it won't make things better. You need some kind of heating in the garage for the opener to work properly. You may leave a door into the home that opens into the garage to partially warm up the garage, but your heating bill will be very high.

Don't force it up either. You may just have to park your car outside or leave it totally open until warmer weather. Being minus 25 F is pretty cold. The garage door opener is rebelling at being so cold and it refuses to work.

You need to pull the emergency disconnect rope hanging down from the traveler on the door. Then move the door by hand to see if the tracks are binding and that the springs are intact and working. The problem may be the door and not the opener. Most doors that act the way your does have a broken spring.