Hi Treeman00....I live in upper Michigan and I am into snowcats and snowmobiles. There is no law against running a snowcat on a groomed snowmobile trail in Michigan, however, I would not advise it. You will not be accepted with very much kindness from the local groomers and the snowmobilers. High speed sleds and big fat slow moving snow-cats on the same trail don't mix. There are far too many close call's and accidents involving sleds and groomers on Michigan snowmobile trails.
Now, if you want to run on "Non-Groomed" trails, that's a different story. The chance of a snowmobile running into you will be far less, but trying to fit a big cat down a non-maintained trail has a new set of problems, typically, you will find they are not wide enough, have too many downed trees. and have far to many low hanging branches.
I had a Thiokol 601 that I used for fun, but all my travels in it were done on the shores of lake Superior or down snow covered county roads. Trying to run it on non-groomed trails was just not fun because of them not being wide or clear enough for a 8' wide sno-cat. And the thought of running down a groomed trail and having a high speed sled hit me and all the legal matters that would follow, was not my cup of tea.
That Tucker that you are looking at does have the six wheel tracks, I looked at it years ago, I think it was in Greenly Mich at that time. it was used as a trail groomer.
That's a pic of my 601 on lake Superior. It now belongs to another Forum member.