I was the local manager for a large snow thrower manufacturer's test site here in the U.P. of Michigan for about 6 years.
We would get get 4 hp to 12 + horsepower throwers in. We would buy comparable competitor's models to test side by side with our units. We usually had about 40 machines that represented about 15 - 18 models we made. They were all new at the start of testing.
The snow throwers would sit outside for 24 hours a day from approx. Thanksgiving to around the 1st of April. The only time they would come inside was to do repairs or swaps of test parts etc.
During those months we would have freezing rain to 2 foot snowfalls to minus 25 degrees to a warm 38 - ish degree weather. Again, we never took them inside.
Every morning we would check the oil on all of them, without disturbing the piles of snow or layers of ice on them. Then we would video the starting of each one. Those videos documented (by unit number) how many times we primed the unit, how many pulls it took to start, or how long the starter had to engage to start, and how long it took the engine to stay running without the choke on. They were all manual chokes, so we have hand signals to show in the videos of which setting we were at when. (worked best to get the idea across as compared to yelling over the engine noise to say what setting it was on )
Those videos got FTP'd down to the MFG'r in Milwaukee so the engineers could see them and learn from them and use them as a selling tool.
Most years we would end up with 250 + inches of snow and each unit had about 175 to 250 hours of use on them. We tested on asphalt, cement, gravel, grass, and even snowed over grassy fields. (we had 48 acres to choose from).
The 4 hp models were usually the single stage blower with the rubber on the auger that would both suck in the snow and launch it out of the chute. They did ok.
The 5 hp in a 2 stage model could and many times did keep up with the 8, 10 and 12 hp models.
The diameter of the "flywheel" in the gear case that spins the impeller and auger and the rubber friction disc turned against to drive the tires was a big deciding factor in how far the snow got thrown and how fast you could get from point a to b in X amount of snow.
That and the height and width of the auger housing is what really determines how they work. A 42 inch wide by 26 or 28 inch high opening gobbles snow quicker than a 24 inch wide by 19 inch high opening did.
So, there is not too much to worry about when you hear 5 hp or 8 hp and try to decide.
I myself have had a few 24 inch wide, 5 hp 2 stage models here at home and I have been happy with them. They throw snow just fine into my neighbors yard. ;)
We manufactured various models under the names of: Simplicity, Craftsman, John Deere, Toro, Brute, Yardman, Yard Machines, McCullough, Cub Cadet, Snow King (the odd names that are / were Murray). Murray is no longer around as a company, our company absorbed them for business reasons.