Driving on snow and ice can be a challenge, even for fat-tire bikes. Braking is problematic, and turning on ice is outright dangerous, even at low speeds.
So, after watching some youtube videos I equipped my front tire with a DIY snow chain. The results were mixed: braking improved considerably, but I had to remove the mudguard because of its small tire clearance. Also, some chain links constantly touched the fork while driving. Most importantly, however, I learned that driving with a chain but no mudguard in slush isn't fun. So, plan A failed.
Plan B was to install studs on the front tire - in the form of 128 8-9/16" screws (because I couldn't find studded 20x4 tires anywhere). After installation, the screws stuck out a bit too much, so I cut their tips off with a bolt-cutter. After 2-weeks of driving on snow and ice - using icers (just in case I slip) and 10 psi for the front tire - I can report that plan B is working out nicely: braking is almost as effective as with the chain, turning is much improved compared to using non-studded tires, slush is no problem anymore, and the rolling resistance hasn't increased by much. While driving on snow I am using assist level 2 more often now, but the large batteries we got are still good for 75+ km in the city at ~20km/h, even at -10C.