Well, I really doubt the motor has any damage at all from running the chainsaw 2 stroke oil. Has it been run in like -20F weather?, I can't recall ever having any 2 stroke oil pour slow in when I've been mixing in the winter, so I wouldn't worry about it too much.
I assume its an older sled? I don't use the injector system at all on my old sleds. Just run premix of whatever 2T oil I have around. If you are really worried, usually you can take the exhaust off with a couple bolts and you can look in the exhaust port and see what the pistons look like.
Old sleds usually sieze because of carb problems or seal problems on one cylinder, or no oil from an injection system. I've never heard of one siezing due to having the wrong oil.
Ian
ps, some of the very latest skidoo motors do require very fancy injection oil, if you have one of those then put the right oil in.