I've never used the snowmobile trails in Eagle River. I have elsewhere in the US upper Midwest, when I owned a snowmobile.
They aren't always strictly for recreation, but actual winter transportation. A hidden network you don't see in the summer, if you don't know what to look for.
A real obvious clue is when you see reduced-height, small scale traffic signs alongside the roads. When the snows come the snowmobile trails become obvious, with trackways easy to spot. Local snowmobile clubs and even county governments publish maps indicating the trails. You can travel upwards of 100 miles between towns entirely on snowmobile trails. With warming huts maintained along the way in wooded areas.
But there are also the games. My favorite was the club poker run. You sign up, get a route card, and go from point to point. The stops are usually restaurants & taverns to warm up. It's funny, having a place packed with people wearing snowmobile suits, some electrically heated (in North Dakota it could be -15 or -20F air temp, wind chill greater on the sled at speed), looking almost like astronauts with their helmets, too.
And that speed could be VERY fast. My own 600cc Polaris triple, which wasn't a racing or sport sled, was capable of just under 100mph. Although I never went that fast, I think 60-65 at most. But close to the ground on bumpy trails that's thrilling enough.
Mostly, though, I just wanted to sightsee, and took my time. Sometimes with one of my young sons along (my sled had a double saddle for 2, and even the passenger handgrips were heated, in addition to the handlebar grips). Other times a friend might come along on his own sled. Safer to not travel all alone in remote areas, should some mishap occur (and with me you could almost guarantee it).
Today snowmobiles have lost popularity, especially with a late or thin snowcover in many areas. Most sleds need some loose snow to cool their engines. A 4-wheel ATV is more versatile except in deep mountain snow.
An ATV can also cross hardtop roads, and even go down them short distances (although not technically legal), as well as travel on private farm roads and across farm fields before the snows come. They make a good hunting vehicle for getting to duck blinds in the Fall, and bigger ones with racks can carry larger game.