I have been told yes, it will spool quicker with a lightened flywheel or aluminum, but I have also been told that you want the inertia there for rotating mass.
A good point - you want the inertia to carry the assembly through the compression stroke, but I imagine if it's a snowmobile engine, your engine is likely a two-stroke, probably not running nearly as much compression as a typical four stroke, you've just come off of a power stroke, and it might not need the added inertia.
Here's what I'm thinking . . .
I expect you'll be turning some pretty high revs, so the less mass you have, the higher up the rev range you'll be able to turn without developing potentially ugly crank vibrations.
As to whether it's aluminum or steel, I don't think it's as important in your case as is keeping the mass down and making sure it's well balanced with the rest of the engine and clutch assembly.
I'll admit, my experience is limited, but I was shifting at 9200 with a 3 main block design that goes back to WWII, a very lightweight balanced assembly and an aluminum flywheel, and it ran smooth as glass.
Do you know Tom Donnely, the guy who ran the SAAB Sonnet? That's a two stroke - He's in Fort Dodge, Iowa, and he was turning some scary revs with that little 3 cylinder. I'd be tempted to search him out and ask.
Looking forward to seeing what you're up to with that little monster.