I've got a Tecumseh 10.5 on my blower and I run GC 0W30 on the slightly over full side on the dipstick . Great engines really if you look after them . My garage is pretty cold so I like to see the oil ready to splash when started cold , that is why I like to use a 0WX grade and fill on the full+ side .
A snow blower generally see's little use compared to a mower so an oil change should be good for 2-3 years . Mine is going into it's 8th season since I bought it new in 2005 .
OP , keep all your cables and chute track lubed as well as the wheel to axle , you don't want things icing or rusting . Fluid film or any light oil is good .