In Hollywood, scenarios are built to make for a good movie. People are stupid and unprepared, and zombies aren't put in snow where they are less of a threat.
In theory, a zombie would become immobile when frozen. It is likely that the ice crystals formed in the brain as a result of freezing would separate synapses to such a degree that reanimation is impossible. Cryoprotectants ( anti-freeze ) could offset this, but the fluids remaining inside the body would continue to prevent motion until temperatures rose above freezing. This cryostasis could perhaps be thwarted by infusing all soft tissue with cryoprotectant solution, allowing animation even in freezing weather.