If I had to guess, your snow machine is a 4-stroke engine, which means you should absolutely NOT use the 2-stroke oil/gasoline combination.
If your snow machine is a 2-stroke, it might still not be very wise, but it'll work. Two-stroke oil is designed to cool and lubricate, but there are small differences between some types. I have attached a link that talks about the differences a little bit. The main idea seems to be that you'll be fine if both your boat and snow machine recommend the same 2-stroke oil rating.
If you are referring to a snowblower then it is most likely a 4 stroke engine. look up a video on youtube to explain the difference between 2 stroke and 4 stroke engines. huge difference. The answer to your question is no, you can't use 2 stroke premixed fuel on a 4 stroke snowblower. The reason why (if you care to read) is that 2 stroke engines don't use conventional motor oil for engine lubrication, they get there lubrication from the 2 stroke oil you mix with the fuel. 4 stroke engines dont use this method of lubrication, instead you just do periodic oil changes in which you pour 4 stroke specific engine oil like 30w or 10w-40 straight into the engine block.If you use 2 stroke premix Your engine will get too much oil and cause it to run like crap if at all, on top of smoking alot.