The manual for my 1974 Tec SnowKing (8HP) says to use straight 30 weight above 40 degrees F, 5W20 below 40.
The manual for my 1988 Tec SnowKing (8HP) says to use straight 30 weight above 32 degrees F, 5W20 or 5W30 below 32 F. It also says you can use straight 10 weight below 32F. Below 0 degrees F ONLY: 10 weight diluted with 10% kerosene or 0W30. This manual specifically states to NOT use 10W40.
FYI- These manuals are from my Ariens SnoThro- which can also be used with other attachments for cutting grass, that's why there is information for operation above freezing.
I have been using 5W30 in both for years (Winter only). You should be able to find 5W30 just about anywhere- I get mine at WalMart. Any 5W30 will do.
Some on this and othe boards use synthetic, but I never have. Shouldn't hurt anything except your wallet just a little more.