I have had recurring problems with my washing machine drain freezing during extreme cold. When the washer goes into the drain cycle, the water comes up through the floor drain under the washer. The pipes are sealed into the crawl space by the floor and can not be accesed. I assume that the water is freezing in the trap that must be located under that floor drain. I have tried pouring boiling water into the drain, but that has not helped in the past. I have generally had to wait for the weather to warm up.

Drain lines rarely freeze under a slab. Does the rest of the house drain OK, if so I'd think your washer drain line is clogging up with lint.