I'd imagine 2.5HP would barely get over the friction of the tread bearings/rollers, probably require at least 10x that to make progress on anything other than level ground at more than walking pace.
The track isn't
that lossy, although you're not far off.
A good comparison machine would be Ski-Doo Elan (1971-1996): weighed about 140 kg, with a 12 to 24 hp motor.
I drove one lots when a child, and although nothing like the current speed beasts, it could drag a sled with people and skiers behind it at respectable speeds. I'd guess 12 hp ≃ 9 kW would suffice for the snowmobile to be useful, and reach speeds of say 60 km/h on ice or hard-packed snow, and be able to climb at least modest hillsides.
Something like 5 kW would probably be unable to pull anything, but might still work as a single-person conveyance, say something to let kids ride in controlled conditions.
(The best thing about the Elan was that if you got stuck, it was light enough to lift solo. I don't mean clear off the ground, I mean enough to turn it around and return using the track you already made. If you had a snow shovel with you, getting stuck wasn't that big of a deal. With the current speed beasts with their narrow tracks and heavier weight, I'd be much more worried about getting stuck in snowdrifts. Which reminds me: weight distribution is also very important to make it ride-able. You don't want it to be so front-heavy it becomes a snow-submarine, nor so front-light the skids won't steer.)