I'm not sure how the State of Montana classifies a proper snowcat like your Tucker. It is technically not a snowmobile per the MT Annotated Code which states:
*****(11) "Snowmobile" means a self-propelled vehicle of an overall width of 48 inches or less, excluding accessories, designed primarily for travel on snow or ice, that may be steered by skis or runners and that is not otherwise registered or licensed under the laws of the state of Montana.
On top of that, snowmobiles require titles to register here. I lack a title for the snow-trac so I just put the orange triangle on the back and haven't had trouble from the sherrif, border patrol, or USFS. Of course I haven't pushed my luck by crowding groomed trails either, just USFS roads and a remote, non-paved county road. Let us know what you find out if you take a crack at regitering in MT.