Do they run and drive??? If the guy says they run on spray and just need some carb work... walk away. These 2 stroke snowmobiles can start, run,and seem fine but you really need to fully warm them up and ride them to get an honest idea of the condition of the motor. Take a compression check. Its quick and simple to do and will tell you a lot about the motor condition. Look the tracks and suspension over good. These are high wear and tear areas. If the sleds have steel tunnels and belly pans look them over for rust. Look around the ski spindle mount for damage. These areas get damaged when you hit some thing at high speed.If you never owned a snowmobile they are kind of a "love/hate" thing. They are a lot of maintainance and can be temperamental.
Get a close look at the switches and make sure the wires are in good shape. Being that they are 30+ years old, parts are getting harder to get. Make sure the gas tank and if it has it, oil reservoir to make sure they are empty. Last thing you want to deal with is stale gas and bad oil (if its oil injected). If there is gas in the tank still, then more than likely assume the carb has gas in it and needs to be cleaned out.
Also check the hood and other body work for cracks. If the hood is cracked, it's probably been beaten up and had a hard life. If the windshield is missing, there may be a reason for that as well. If the odometer on the speedometer or tachometer does not work, then I would walk away. No telling how many miles or KMs are on it of the odometer is shot.
Take a close look at where the skis connect to the sled itself. If it looks like any of the metal has been rewelded or cracked, been ran hard and walk away, do not buy it.