It can work, don't skimp on the heater...and get your birds acclimated now to using horizontal nipples.
This has worked well for me for 5 years now:
https://www.backyardchickens.com/articles/aarts-heated-waterer-with-horizontal-nipples.67256/
Hmmm, you can hope...but there not much about...
Gonna be hard to ventilate that tiny coop without drafts.
https://www.backyardchickens.com/threads/ventilated-but-free-of-drafts.1048597/
It's also pretty darn small for 4 birds in your climate.