This is a 2-stroke 3hp Snapper single-stage snow blower. The model number is 3201s but there are many different models that are nearly the same. It looks like Snapper made almost the same model, with slight differences for at least 10 years but I think they last made them in the 80s. I guess this is almost 30 years old, but I can't tell for sure. This one seems to be one of the better ones, because it has the electric start option.
Step 1: Assess and Tear Down
When I got it home, my first troubleshooting step was to put a little gas in it and pull the cord to see if it would start. Nothing worked, so I pulled some more and all I succeeded in doing was breaking the handle free from the rope, which ran away back inside it's hole. I tried the electric start and while that didn't start the motor, the electric motor was very strong and worked perfectly.
I took off the top and bottom covers, which were in decent shape. They had some cracks in them, and a few of the fastening holes had broken tabs, but they would still stay on and keep snow out. The top cover is held on with just nuts and studs at the top end, and carriage bolts from the inside of the auger housing. The housing has square holes that hold the square collar on the carriage bolt and prevent them from turning. Once the bolt loosens up it will spin freely and you will have to hold them tight to the housing. I had to use a lot of WD-40 to unfreeze these bolts and I ended up holding the carriage bolts with some locking pliers. Since a lot of snow builds up on the top of the auger housing, I expect most snow blowers would have the same issue.
I was hoping to find a service manual, but there aren't any online. I found the original operating manual here but that is only 3 pages so it isn't much help. I also found some parts diagrams on this website. They can be helpful, if only to see how things come apart. I also found this better operating/service manual but that only shows how to service the auger belt and fold up the handle for storage.
Update: I found the parts manual for the 3200, 3201, 3202 and 3203 models. I attached the PDF below.