LateToTheParty
Didn't want to come
The biggest those come in that would work for the 20" wheels the OP desires are the 305/55R20 which are a far cry from the 37s which were asked about.I'm going to throw a different name out there, the Nokian Outpost AT. It's not super aggressive looking, the compound I believe is a bit softer but if SNOW and wet performance in an AT is what you're looking for I doubt you'll find better. They are 3-peak rated. They are also a very lightweight tire probably due to lack of aggressive sidewall and extra rubber. Nokian is a Finnish company and I believe their tires are made in Finland. Anyways if there's going to be a brand/company that I trust or would expect to understand the dynamics of winter driving it's probably going to be a from Nordic country. Their dedicated winter tires have an outstanding reputation.
Nokian Tyres Outpost AT - Extend your adventures / Nokian Tires
The Nokian Tyres Outpost AT offers supreme traction in all conditions, extreme durability and puncture resistance, and increased service life so drivers can extend their terrain, toughness and travel.www.nokiantires.com
However of your list of 4 only the Falken AT3W is worthy of your consideration in snow/wet performance. The Nitto's and BFG I would absolutely cross off the list. I think your list should include the Falken AT3W, Toyo Open Country AT3, and the Nokian Outpost AT. That would probably be my top 3 with Nokian as the likely best performing one for your use.
These may be an option for someone looking to stick with stock or similar sizing, but for the rest of us, they're not a viable option.