I have the Nest doorbell and would suggest that it makes the most sense if you are already heavily invested in the Nest ecosystem. I love it so far, although paying $5 per month for storage sort of sucks.
I would think that the only thing the cold would affect is a battery. Arlo really suffered from this. The Nest is hardwired and Ring makes both battery and hard-wired models.
I've been building my automation/security system using this, btw:
https://www.home-assistant.io/