Any battery operated device in the typical smartthings price range will probably say that it works down to freezing but not below. 
It’s quite easy to add a device inside the house, though, which can pick up the vibrations and/or electrical signal of the existing wired doorbell and that’s what most people use in those kinds of climates.
If you are in the US, Nexia has a zwave doorbell sensor made for exactly this purpose.
People also use a number of DIY approaches which typically involve a vibration sensor or a dry contact device. You can read about those on the quick browse lists in the community-created wiki. Go down near the bottom of the page for the “project reports“ section and choose the list on “doorbells.“ 