When I open the door, if I have 3" or more of snow against the door and drive in or out, the snow will fall where the rubber threshold meets the floor. That is all it takes for the door to freeze to the floor just a tiny bit. After many cycles, the threshold will be loose. So before the door gets closed i shovel the first 6" away from the door so it won't freeze down.
I think my problem is to much heat or maybe to little heat. I heat my garage continuously to 42 degrees. That seams to be enough to melt frost, ice and snow on the door but not enough to melt the snow under the rubber threshold.
That is why i would have concerns with forcing water under the door and not down a drain.