When starting a snowblower, the best time of the morning to do it is always going to be as early as you can. One hour after sunrise should be optimal in most cases, but it depends on local regulations and how understanding your neighbors are.
That’s when the engine isn’t cold, and temperatures are high enough for a seamless start-up. Plus, starting early gives you plenty of time to clear your driveway or sidewalk before work.
You should never start a snowblower too early because you’ll likely annoy all your neighbors with the noise. If you need to use a snowblower early, I suggest using an electric model, as they’re quieter.