This is a new area and growing so I am sure it will take time to work out reasonable rules and behaviors. I recall when people were loosing their minds over how that new fad snowboarding was going to ruin skiing.
I have an electric fat tire bike (
https://www.biktrix.com/collections/bikes/products/biktrix-juggernaut-classic-original) mainly for commuting and for use on groomed ski trails (Nordic Ski Patrol) when the snow is firm enough. But I do like to play as well, and an e-bike on snow is more fun than I can put into words.
Washington has one of the more restrictive laws on this; no e-bikes on 'unimproved' train (e.g. trails) unless approved by the land owner/manager. This helps keep them off of hiking trails and out of the wilderness but allows for some flexibility.
I would note that an area near me has managed to develop a mix of hiking trails and single tracks as well as some equestrian use, and there have been little to no problems that I know of. I asked about e-bikes and the response was "you are more than welcome". I attribute that level of success to the managers and community of users being as inclusive as possible, and making efforts to communicate and make reasonable accommodations.
e.g. hikers encouraged to avoid the single tracks but if they do use them are to give way to bikes, and vice versa. They post when the trails are soft/muddy so horses/bikes might cause excessive damage and most follow the posted recommendations so no enforcement is necessary.