Douglas Harper's Etymology Dictionary
proprietary name of a type of snowmobile, 1961, from ski.
Wikipedia
Ski-Doo is a brand name of snowmobile manufactured by Bombardier Recreational Products. The first Ski-Doo was launched in 1959. It was a new invention of Joseph-Armand Bombardier. The original name was Ski-Dog, but a typographical error in a Bombardier brochure changed the name Ski-Dog to Ski-Doo.
The first Ski-Doos found customers with missionaries, trappers, prospectors, land surveyors and others who need to travel in snowy, remote areas. The largest success for the snowmobile came from sport enthusiasts, a market that opened the door to massive production of snowmobiles. This popularity led to skidoo (sometimes ski-doo), with the derived verb skidooing (or ski-dooing), becoming the traditional generic term for snowmobile in much of Canada.