Bringing this one back again. Obviously, the idea of anything resembling a traditional snowmobile intended for an adult rider weighing 200 lbs is pure fantasy at this point. The closest you'd find would be an under-powered snowbike or kids toy. But an ultralight alternative to the typical 150hp/500lb mountain sled, something that would be just as capable and more fun to ride, intrigues me, and there's a lot of good discussion here.
Here's my thoughts on motors: I think fan-cooled is the way forward, but we're pretty ham-strung by the fact that there's been no new technology built into a fan motor for around 20 years. The Poo 550 is a decent motor for what it is, and 65-ish HP can still be fun; call it a good starting point. I'm not sure what the weights are, but I'm guessing the Cat Blast motor weighs about the same; could be less, but it's gotta be more when you add coolers. It adds a lot more when you consider the snow build-up it's going to bring to the tunnel. But it's definitely more powerful, and probably more efficient. I suspect if cost were no object, Cat would have built a new fan motor for the Blast, but cutting a CTEC in half was too cheap and convenient to ignore. I don't think you could build a fan motor that could rival even 600 twin power levels, but 100 HP could be a good target for a ground-up fan motor build. Heat is the big problem: build a fan motor just like a performance liquid-cooled, and it'll burn up almost instantly. But with thermal coatings on pistons and heads, EFI, and more modern cooling design, there has to be room for growth. Unfortunately, I'm getting more into a pipe dream on that...
I have a couple ideas for the chassis. The most pipe-dreamy (for the moment) is carbon fiber. It's easy to say throw out CF and say "presto, weight disappearo!" but I'd guess an easy 20 lbs or so over a traditional aluminum construction. I suspect the best approach to balance weight, durability, and cost would be a one-piece CF bulkhead and partial tunnel. To that would attach a subframe containing the motor and suspension mounts, and in the rear, a replaceable tunnel and running board assembly. It may not actually be that different from current chassis, just replacing big chunks of structural aluminum with CF. A little more down-to-earth, I wonder if there could be weight savings from a MacPherson strut setup. Doo used that with the Freestyle; not sure what the drawbacks would be, but it could be worth some trade-offs if it offers significant weight reduction.
Going to the back end of the sled, I'm going to go back to the Blast. A monorail with a track in the 140" range may be the lightweight sweet spot. For certain, 155+ tracks with >2" paddles wouldn't be necessary: you don't need as much when you don't have that extra 100 lbs (or more) to push around, and you'd have more track than the smaller/lighter motor could run effectively anyway. I think somewhere in the range of a 141" x 2 track would be perfect, and narrower would be good too: 14", maybe even as little as 12". You're really playing with riding characteristics a lot between a monorail, narrow track, and overall narrow track, but I think you could come up with something good.
If I had bottomless pockets and started building today, I'd be looking at something like an AXYS bulkhead, EVO tunnel, tweaked 550 fan (unless I could use the Blast engine without adding more than a few pounds), Blast M skid and track, quickdrive2 belt drive, lightened P-85 / TEAM clutch, and cut down and lightened AXYS bodywork. That would get you halfway to what's possible: to really get where we want to go would required a top-to-bottom build, something that would take the resources of Poo or Doo and a big investment. I think my frankensled would easily hit 350lbs dry and be a hoot to ride, but to have the same capabilities as a typical 800 would require dropping significant weight and picking up a chunk of HP (again, possible, but beyond the abilities of an independent builder). Depending on the conditions and rider preferences, superlight but underpowered would be more fun at times, but hard to make a complete argument for if the lack of power and track were a constant limit. An AXYS 850 is about 165hp, and around 500lbs ready to ride. Add 200lbs of rider and gear, and you've got 700lbs to 165HP. That translates to around 4.25 lb/HP. Now take a 300lb sled dry, add 50lb of gas (shouldn't need as much), 200lbs of rider and gear, and you're at 550lbs; you need 130HP to match power:weight. That doesn't account for less parasitic loss from a smaller/lighter track, but the indication is still that a truly lightweight sled may mean a weaker power:weight ratio. Still, how many guys rave about how much more fun 200+HP Yammi Vipers are to ride than lighter but less powerful 2-strokes? There's definitely territory to be explored. I say build it, and they will come.