Steel construction is not composite construction.
I have not seen many snow mobiles in person, but in general the trick for weight saving is in integration.
I can imagine the thing might get lighter if you can toss the steel frame all together, and just have a carbon monocoque on which you bolt the engine, track and steering.
This does not need to be cored, many pieces can benefit by adding stiffness due to design. Mounting points can be beefed up to accept and spread loads.
When you are up to that, manufacturing techniques are critical. You want lots of carbon, and little resin.
An other option is to rely on the steel frame for all loads, and just close things with very thin carbon paneling.