I had a snowblower that blew a HG last year. At first it was just a little hard to start but after the leak got worse it would die under load.
When you engage the blades the motor sees a heavy load for that first moment while the stationary blades begin to move. This could very well be a compression or a fuel related problem as something can't keep up with the load. Because fuel problems can be a little harder to track down I highly recommend starting with a compression check on your motor so you can rule out head gaskets and other compression related issues (I know, a leak down test is needed to rule out valve issues). If there is a compression issue and you are trying to fix the fuel system you are in for a lot of wasted time.
I am not saying that I think the problem is with compression. There is a certain methodology to diagnosing motor problems. Motors need air, fuel, spark, timing, and compression to run. Compression and timing are the easiest to rule out if you have a compression gauge and timing light. Spark is a little complicated. Having spark and having good spark are two different things. Air fuel issues are pretty tricky to diagnose. That's why you will see that many of us back yard mechanics will just go ahead and rebuild a carb just to see if it helps.