Minimal effort chain cleaning
Rain, hail, and snow don't hurt a chain. Salt makes it rust, and dirt wears it out. 

Salt: You won't get all the salt out without removing the chain from the bike. The chain is doomed. You can, however, easily delay this till spring with regular application of wet chain lube. A bit of rust won't hurt if you ride regularly. 

Dirt: Given that the chain only has to last till spring, a quick clean with a chain cleaner (as suggested by @meager) once every few hundred miles will be fine. 1 minute of cleaning, 1 of re-oiling is enough.

Come spring, splurge on a shiny new chain. If your budget is really tight and you don't want to buy a new chain every year, keep the old one for next winter. When you take it off, give it a really good clean (off the bike), soak it in oil and store it over summer. 

However, there are a lot of reasons why a new chain every year is a good thing.