I never thought about flushing out the salty snow, but I will be doing that from now on. My new house is on a cul-de-sac so I get an extra large pile at the EOD.
This rust appears to be from sitting in a pool of the salt water. I have an Ariens ST504 that I redid the bucket on 7 years ago. More often than not I fog it with some oil that I have laying around after I dry it out with a heater. It has very little rust on it.
I always start out clearing my EOD drive first. This is the most wet, salty, sand gritty snow that is bad for snowblowers with metal buckets and augers. After clearing EOD, I go over driveway and sidewalk with fresh snow to flush it out. It is quite effective technique and requires no additional effort. Before putting it away, I run the auger/impeller dry without feeding any snow. This will fling some stuff off the auger and impeller. If you're really OCD, you can use pressurized air to clean the entire snowblower off, be careful pointing it at fragile or sensitive seals. The other alternative is to use a leaf blower, which has much lower air velocity.
Salt and water by itself is fairly benign. Mixed together, they are a quite a corrosive force. Corrosion is a factor of time, concentration, and temperature of the salt water. If you have eliminate or reduce any one of these factors, it will reduce corrosion. You can't control temperature, but you can control time and concentration. The key is in drainage.
If you bring a snowblower back into a warm garage, the salt water will start eating away at the metal parts. I have a tracked snowblower so I can tip the bucket housing back and keep it off the floor and not have any pooling of water under it. It will stay tipped back and not go anywhere. If you have a wheeled model, you can put a 1x4 piece of wood, or non-metallic part under the skids to get the bucket and scraper off the ground. The snow will still melt, but at least the water will drain away, and not collect around the scraper and skid shoes. Drainange reduces the concentration and the time the salt water is contact with metal.