up here in Oregon, winter has been here for about a week... it's going to be hell frozen over this year... regardless of the unfrozen zombies... if you're in frozen snowy area, don't worry about detection, first priority is staying warm, they'd be frozen anyway
I just moved back to Utah after a number of years behind the arizona sun curtain and I instantly got hit with a major cold. Been suffering under it for a good week now and its pretty miserable. We made sure to find a place with a fireplace but lucked out and find one in the bedroom!
Anyway, soup, blankets, heaters and someone to help keep me warm, those are my winter survival tips
It's quite possible it would kill them by shocking the nervous system so hard they short out essentially or, worst case scenario... They freeze, rendering them complete inanimate. Thank god I live in Vermont. : )
Colder areas would generally be safer for the reasons provided, but it is essential that you and/or your community are self-sufficient, because the damage around the other areas surrounding you might be so significant that you might not be able to get supplies for a while.
Freezing to death could become a big problem too, if that's the case.