Always thought winch cables to be the same as Rock Climbing ropes when it comes to washing..? Soap is the worst thing you can put on them/clean them with!
The good Winch cables are are Dyneema now and as far as I know soap shouldnt affect them at all.
Ive had mine about 2-3 years now and had a lot of real work outs and although im too lazy to take it off the spool i always hit it with soap & the geurney, I do however also have a spare cable in the car whenever I go offroad just in case.
I picked my last one up on ebay for less than $80.00 for 30m ( i belive 12mm dyneema) I just followed heaps of auctions and set my price at max $78.00 and eventually won one.