Just joined to chime in on this discusson. Some of the newer Synthetic Outboard 2-cycle oils claim to work both ways, at least according to the lables. I bought a gallon of this stuff for $1.50, still sitting in the garage.
As far as snowmobile oil. I have an old Lawnboy utility mower I picked up at a thrift store for a couple of bucks a few years ago mainly out of curiousity if I could get it running. Needless to say I got it running. I mowed my lawn a lot using up a variety of old 2-cycle oils that were floating around (from chainsaws, weedeaters etc.) the first year. While up in Canada I picked up a 4 liter bottle of snowmobile 2 cycle oil. Seeing as that the mower was basically free, I just use a premeasured mixer and use this in the Lawnboy. Been using it for the last two years and haven't had a problem. I just follow the Lawnboy's advice, use 4 oz of Lawnboy oil per gallon and if not using Lawnboy oil use 8 oz. Seeing as that the modern Snowmobile oil would probably be good enough on its own in a 4oz mix (gotta realize this mower is pushing 26 years old, oil probably has improved in the last 26 years), I may just start dumping 4 oz of this and 4 oz of the Synthetic outboard in the gas until I use it up (since it claims to work for air cooled engines). Course this thing is running really rich by modern standards so in that old an engine it probably makes less difference than it does in the modern ones. Those ratios if I recall are 32:1 and 16:1.
As far as the Snowmobile oil in the Lawnboy, compression is still good after about two seasons of using that stuff, and the mower actually starts pretty good on it, usually in one pull, even with 8oz of oil in a gallon of gas (and really doesn't smoke as much as you'd think).
I should note I usually mix some Marvel Mystery Oil in with the gas when I fill up the big can to keep the carbs clean on the other mowers. When I mix the Lawnboy gas it gets that gas then I add the two cycle oil to it. Perhaps if the Snowmobile oil would gum up the carb, the Marvel prevents it, who knows.
I'll play it safe with my string trimmers (they're newer, don't want to mess them up), chainsaws? Well they don't run anyway, I've gotta clean the old gas out of them, I don't use them enough.