Does rain or cold fronts turn off trout like they can bass? I am curious about that and cannot find information, so what is your all's opinion on the matter?
I think some of those same effects can definitely come into play, but the relationship can be pretty complicated. Like Louis said, a wet day can mean that hatching bugs take longer to dry their wings and take off, giving trout better surface-feeding opportunities and making them more active, or at least more visible. Some other insects prefer foul weather for emergence, which again can spur trout activity.
Also, during the hot months of summer, a cold front could lower water temperatures back into the comfort zone for trout, improving the fishing dramatically. (Same goes for the coolest part of the day, by the way.)
Despite these exceptions and counter-examples, I've always felt more optimistic about trout fishing under the same kinds of weather conditions that are good for bass (very stable weather, or with the barometer falling). The effect probably isn't as strong as it is with bass, because trout probably need to eat more regularly. Most trout eat mostly small invertebrates, meaning they need more prey to fill up than a bass that eats a bluegill. Also, in streams they're constantly swimming and usually can't just go sit in a quiet corner and digest.
I don't have much more than anecdotal experience, but Jason may know about scientific studies.
I haven't run across any, though I haven't searched for that in detail. In general, it's amazing how little attention has been paid by scientists to the kinds of things fly fisherman would think we're studying. This one of them. Another one scientists haven't really looked at is the way fish can be selective about some tiny thing like a Trico and ignore everything else that comes by.