Check your local regulations for snow mobile trails...
It is not usually a good idea for snow cats and snowmobiles to run on the same trails, unless they are wide enough for you both to pass.. Also you are not going nearly the same speed as they are, and your a hazard if you are not seen. A slow moving vehical sign on the back of your machine is a good idea, as are a strobe light on top of the machine. Visbility for others is what you want. DOT reflective tape like on semi trailers is good too.
Private land is the best.. I have quite a bit here I can run on. My machine is registared as a snow mobile, but is actually too wide to be. I also am a state certified groomer operator...to help confuse the issue when running mine on snowmobile trails. This was not exactly "planned", it just sort of evolved.
Road ditches are a good avenue as well. A tall flag mounted on your machine will help with visibility there.
Do all you can reasonably do to be visible and be very aware on trails with sleds. Rearview mirrors are a great idea as well, so you can see them before they run you over.. so you can get out of their way.
First, get to know the laws/regulation of your state and area..
Regards, Kirk