Human being are endothermic, or warm blooded. Our bodies generate their own heat allow us to survive in temperatures where cold-blooded creatures cannot. Still, if the body gets too cold a condition known hypothermia results. As the condition progresses, the body systems begin to shut down, organs fail and, eventually, death results. Additionally, if exposed to subfreezing temperatures long enough, the human body will freeze solid. (It is mostly water, after all.)
Given these facts, I think it is a reasonable assumption that a zombie exposed to the elements would be stopped prolonged cold weather. However, the stoppage might only be as long as the cold weather holds out.
If the zombie infection was caused by a virus or fungal pathogen, it is likely that the cold weather would not be sufficient to destroy them. Both viruses and fungi have been known to go dormant for extended periods of time when conditions are not favorable for their survival. When the conditions change, they reactivate and go back about their business.
As a result, a previously frozen and apparently “dead” zombie might actually be in a sort of undead hibernation.
On the other hand, anyone who has seen the import film “Dead Snow” knows that those zombies were not hampered by the cold. It should be noted, however, that those zombies were created by a curse, not a biological agent. When dealing with “voodoo” zombies of any sort, applying scientific reasoning is difficult at best and practically useless.