There's lots of debate about chain washing. I, along with most chain manufacturers, feel it usually does more than good. The key to good chain life is to prevent the kinds of problems that chain washing tries to cure. For winter riding (please consider the source here, I make chain oil, and am highly biased) you're best off with a wet oil based chainlube which will keep salt and water out of the chain. Or you can use a dry lube, but you'll need to rinse and dry the chain and re-apply often.

You can usually keep road chains reasonably clean simply by dry wiping from time to time. Or, if a thorough wash is required, the best method involves removing the chain and washing in mineral spirits or an appropriate solvent off the bike in an old coffee can, doing multiple rinses to be sure all (or most) of the silt is removed, then drying completely before relubing.

The problem with chain washer gadgets is that they don't do an effective job, washing dirt into the chain as much as they wash it out, because unless you change the fluid a number of times you're just circulating the same crud. Also they don't provide an easy means to dry the chain, which means that the spaces within the chain remain full of solvent, and newly applied lube won't penetrate to where it needs to be. (By way of anology, imagine wiping up a spill with an already soaked paper towel)

The damage to your chain can't be undone, but you can prevent more by keeping it oiled, dry wiping it as needed and staying ahead of the problem.