well it might not be a good idea if it is cold, but if it is really infested with the fleas, and depending on how big the cat is, you might be able to try it, use warm water, and dry it very good... would a hair drier not too close to it scare it? then maybe give it some warm milk? and then a nice warm cozy blanket. inside the house it should dry and be ok. try not to wet its face... for the goop in the eyes, try a cotton ball in warm water, and then lightly wash the stuff out of the eyes, I bet that will make the kitty feel better too.
keep us updated.