Ice/ cold water gets rid of the lactic acid in your muscles quicker allowing better and quicker recovery. Alot of motorcycle racers do the same thing.
I've not been brave enough to try it myself! I tend to have a shower as cool/cold as I can bare it. It definately helps though.
Lactic acid will be dissipated in less than an hour, according to this link: http://www.wikihow.com/Reduce-Lactic-Acid-Build-up-in-Muscles The soreness is caused by the micro-tear of the muscle fibers. "...This causes inflammation, swelling and tenderness as the muscles repair themselves..." And what's the cure? Here's another link, written at least by an M.D.: http://www.thedoctorweighsin.com/to-treat-sore-muscles-heat-or-cold/ The actual method seems controversial. If you search/read enough on internet, you'd get all sorts of answers. But if you accept the hypothesis proposed by Wiki above (i.e. muscle tears/inflammation), then it presumably can be treated like other injuries - cold treatment, in which case a (ice) cold bath may make sense.