Living in Alaska I can say that you can use an exhaust brake on snow and ice - carefully! I drove it to work every day for a winter.
The vehicle must be in 4wd to spread the load to all 4 tires. And if it is a 2 stage brake (my first stage is a flap in the exhaust beyond turbo, second and more powerful is Jake brake type mechanism in cylinder head involving extra exhaust valve), use only the first stage unless you have confidence in the surface.
I had some portal work done at a dedicated Unimog dealership in Karlsruhe in 2017. We told them to replace brake pads if worn 50% or more, after 94,000 miles. They said they were still good. I use the exhaust brake obsessively.
Bottom line: on snow/ice always use 4wd, carefully use flapper brake if indicated, don’t use Jake type brakes.
Just my experience.