Put me in the "No ATVS on Winter Trails" camp.
In Alaska to ride winter trails on state land or on trails maintained with state funds you have to have a $10(for 2 years) snow vehicle decal. ATVs with decals are perfectly legal but they do horrendous damage to trails.
Now, we don't have groomed trails nearly to extent of most other states but what trails we do have are important to people who live or have businesses off the grid. Those folks rely on smooth trails for freighting supplies and building materials. Wheeled vehicles tear up trails. Period. In those areas frequented by ATVs, grooming costs are double, even triple and wear & tear on grooming equipment increases.
Our grooming pool in AK is small to begin with and non trail related projects are eligible for that money which means many of the groomers pay out of pocket. ATVs incur far more costs to maintenance than they contribute in decal fees (which are ridiculously low to begin with)
I'm a recreational rider and I only use trails to access backcountry. I can live with ruts here and there, but there have been days where a day in the hills started with 20 miles of smooth trail only to become a torturous, shock wrecking ride back to the truck because 3 or 4 guys on ATVs thought whipping brodies all over the entire trail system was a killer idea. Did they break the law? Nope. Did I wish a slow death upon them? Yup.
I own two ATVs. I just don't ride them in the winter. There's a time and place for everything, and for an ATV, winter is not the time to be on dedicated snow trails.