Make sure fat bikes are allowed on the trails you plan to ride. Check the local trail alliance website or message them directly.
Use a fat bike. Many trail networks stipulate minimum tire widths, usually 3.7″. Anything less and you’ll cause ruts and damage the trail.
If you are on a fat bike and still creating ruts, stop riding. Either drop your pressure lower so your fat bike tires float, or come back another day when conditions are better. 3-5PSI for soft snow, 5-8PSI for hard packed snow.
If you have to push your fat bike, do not walk on singletrack. Walk beside it  (even if it’s powder) and roll your bike on the trail. If you leave deep foot prints (“post-holing”) they damage the trail for others.
Respect other trail users. Fat biking is still relatively new, and the more positive interactions other trail users have with fat bikers, the better our reputation.