Thankfully for me, this didn't actually occur to me, though I did have a similar experience.
Turns out her home, like many others in the midwest part of the USA, was beset by rain, then snow as well as falling temperatures. This left a lot of water near her garage door, which froze as the temperatures fell.
The garage door had gotten stuck to the ground, but the opener didn't know that and kept pulling the door. Something has to give.
Turns out in this case it wasn't the ice!
The garage door actually got pulled away from the opener mechanism. It pulled the bolts right from the garage door.
As I mentioned, we did have a similar thing happen the first year we lived in our house. I did the same thing my friend did, and heard a weird banging noise before watching the garage door go up. In our case, only a part of the garage door had frozen to the ground, so it was able to pull away, but not before bending the bottom part of the frame.
A few months later, we had someone out to look at the garage door (for other reasons) and he simply straightened it out by hitting it with a rubber mallet a few times, putting it (for the most part) back into position.
My friend wasn't so lucky. She has a $100 repair to re-attach the door to the opener.
Her repairman did give a tip and that's to spray the bottom of your garage door with Pam which will reduce the ability for it to seal during icy condition.
Since our incident, I've actually been more dilligent about keeping the area dry. Where we had run into problems is when melting occurred, leaving the driveway wet, but then re-froze during the nighttime temperature drop. Since then, I try to squeegee off as much of the water as I can away from the door before it re-freezes. This has worked well.
In any case, if you have a garage door that gets water around it during the winter, keep on top of it before you end up with a ‘stuck' door!