Yellowstone National Park is in the final public comment period for their new(est) winter use plan. Given how long this process has taken, and the good chance of it being controversial, comment now. Whichever plan is settled upon is likely to be in effect for a while.
You may comment (easily) and read the very long document here.
There are four identified options. The first is to do nothing, which is to say allow the current lack of a plan which explicitly permits non-official motorized use to continue. This would provide for no use of snowmachines on the unplowed roads south of the Mammoth/Lamar area. It would end snowcoach travel on those same roads, which would presumably shut down winter operations at Old Faithful. As the document notes, it would manage most of Yellowstone just like Glacier, Crater Lake, and other major western national parks are managed in the winter; as Wilderness. It would be a big change.
The other three options allow for various amounts of snowmachine and snowcoach travel. Each restricts the volume and nature of traffic quite a bit, and I do not believe the average visitor would notice much difference. Certain guiding companies and Xanterra (which operates the Old Faithful complex) would see differing economic impacts between the various options. The town of West Yellowstone, out of which the vast majority of this traffic originates, would see economic impacts as well, especially if the no action option is selected.
It is interesting to note that snowbiking and kite skiing are not on the table for authorization. Both are prohibited in the park at the moment, and while letters encouraging action of this issue might make it more likely to come on the radar in the future, it is probably a good idea to also specify a preferred alternative, least your letter be cataloged as unrelated and not counted towards the issue at hand.
It is interesting to note that were motorized traffic forbidden, the issue of allowing snowbiking would become primarily academic. The NPS currently sets classic tracks in a few locations (going south from Mammoth towards Indian Creek, for example) but does not groom for skating. Baring the packing of the roads by snowmachines, conditions for fatbiking would be rare in the typically cold and low-moisture environment of Yellowstone.
I commented to endorse the no-action option, and did not mention fatbiking. The park is surrounded by national forest which allows snowmachines and is thus excellent for fatbiking. Yellowstone has many attributes those places do not, and should be kept as wilderness-y as possible. The bison have a hard enough time in the summer, and insofar as the future of Yellowstone must include a drastic reduction in private vehicle traffic June-September, the correct first step is with winter.
Ride your fatbike somewhere else.