Found this educational & fun video on youtube comparing a 4x4 car on summer tires vs. a 2wd car on proper winter tires:

https://www.youtube.com/watch?v=atayHQYqA3g

Moral of the story: 4x4 is useless in the snow without grip, and to get grip you need snow tires.

If you ever need to drive in the snow, watch the video. Then get snow tires.