My experience comes from working at a few vet clinics and helping out at a couple of training kennels in the midwest. At home we have a little stone dog yard about 10X30. We can get that kind of cold, and lots of snow, but it doesn't last for months or even weeks on end, so YMMV.
First, don't let the dogs have free choice in and out overnight or when it's snowing. Shovel and broom the runs before the dogs have access.
Then, use an ice scraper to loosen piles and frozen puddles of urine, and scoop them up. We always pretty much cleaned as it dropped, which worked with the dogs not being able to go in and out at will. No smearing or smooshing the mess around.
If the dogs have to have constant access because you're at work, try to scrape a couple times a day.
The minute there's a warm up, hose/disinfect then squeegee the water out of the run.
One place I worked had heated runs, recirculated hot water under the concrete. Fabulous in winter! So if that's ever an option I would go for it.
Hang in there, spring's coming