Here's one data point: Coincidentally (since I just read this thread today after doing so), I decided to put out bath water today for my 3 pigeons, who are living on my back screen porch here in northern New Hampshire this winter (pending construction of an aviary that we procrastinated too long on). It had warmed up to a balmy 30 after a week or so ranging from 0 to the low 20s. Upon seeing the water tray appear, all three headed right for it and (though somehow I'm never looking at the right time to see them doing the splashing) soon water was splashed as far and wide as ever - so apparently they bathed enthusiastically. I see no signs of harm to them!
Disclaimer: I'm new to all this after rescuing my first, apparently a wedding or graduation release, by the side of the road this last June. The other two are a pair adopted to give him company. So I don't claim any great knowledge - just what I've picked up here and on Pigeon-Talk and through Google searches, and what my pigeons themselves have told me.