I know this is an old thread but pretty relevant since it's fall and many owners should be testing their snowblowers now before needed.
Without a primer I believe you should have a choke. Make sure the gas is kinda fresh. Drain most of old gas from tank if it smells funny. Also most carbs have a drain plug or valve on the bowl.
Since I started using Ethanol free gas in my blowers, generators and other small engine equipment have rarely had a starting problems even after a long layoff. Also use some kind of gas stabilizer in your fuel jugs like Stabil or better yet Ethanol Shield brand.
Some people will use True Fuel or special small engine fuel in a can but I never have except when I bought a brand new Husqvarna chainsaw the dealer gave me a couple free cans. Expensive stuff.
I always check the oil before starting, check gas .
If you do everything and it still does not start, of course there could be other reasons. Check the spark with an inline spark tester or the of fashioned way by removing plug and laying it against metal and pull the cord. You should have an extra plug in your toolbox. Or perhaps the choke is out of adjustment. On a Honda you have to pull the side elbow that is connected to carb to check. Fairly easy to adjust.
Otherwise it could be other reasons like lack of compression, valve adjustment, weak or bad coil, etc etc.....but if it was running when parked usually it's the simple things listed above.
I probably missed something so please help me here..... up at 3 am loading up on coffee....