You don’t tell us the manufacturer, so how are we to know exactly what type of lube you need. If you look up the specs for Ronex ED #1, you will see that this is way over kill for a snowblower gearbox. Second, you stated;
From the manufacturer's manual:
AUGER GEAR CASE•The gear case was filled with lubricant to the proper level at the factory. The only time the lubricant needs attention is if service has been performed on the gearcase.
If you are not going to open the gearbox, why throw out the manufactures recommendation?