Anything that cannot generate its own body heat will in fact freeze. Some smaller life forms to include certain fish and amphibians do freeze solid and survive the process, There is however no known case of a mammal doing this. When human tissue freezes ice crystals form on a cellular level which rupture the cell membrane. This causes the tissue to become necrotic and gangrene results. Short answer is barring a supernatural agency they will freeze, and when they thaw there will be no viable cells to reanimate. This does not preclude the virus itself surviving in the tissue, and reinfection via contact with infected tissue, infected objects and surfaces, or reinfestation of areas via migration from more temperate areas is possible and flare ups are to be expected.
I think they would actually have to freeze solid. Usually when people die of exposure it's not because they've frozen solid, it would take a lot to freeze a zombie.
Also, freezing would damage the cells in the brain, and if the brain is what's required to survive (as far as a zombie can, that is) then I think that a lot of frozen zombies would not come back again.