Mountaineers doing technical alpine routes certainly use rock pro under wet or icy conditions. However, the kind of routes they're climbing are typically not the kind of high-angle stuff that you have in mind when you go out for a day of rock climbing. There are people who do things like mixed rock/ice climbing, but you really have to know what you're doing. I've never done any aid climbing, but aid climbing in the rain sounds to me like a really, really bad idea, because often the placements are extremely marginal.
I think there are really two separate issues you want to keep in mind when attempting to apply your trad technique under wet conditions.
One is that lubrication reduces friction, so for example a cam in a flaring crack might not hold if it's wet, even though it would have held under dry conditions. But of course not all gear placements depend on friction. If you place a big hex in a constriction, no friction is required. And even with an active placement that requires friction, the way active gear works is based on the principle that as you increase the tension on the rope, the gear presses against the rock harder and harder, giving more friction.
The other issue is rock quality. Even on well known trad routes, there is sometimes rock fall. A rock can hold over and over again under whatever strain is applied to it by climbers -- which could mean placing gear behind it, or simply using it as a hold -- but one day, it comes loose. For example, there could be a refrigerator-sized boulder sitting on huge, sloping ledge at the top of a single-pitch climb, which everyone has been using as a belay anchor. It's been holding non-leader falls for years just fine. But on a day when it's raining hard, that amount of force might finally cause it to slide off.
Erosion is a natural process that shows bursts of activity at irregular time intervals due to conditions. If you're in the mountains during or soon after a storm, you will often see new rockslides. This is why, for example, there are huge debris-control dams at the bottoms of the canyons in our mountains in Los Angeles. Entire towns have been wiped out by boulders and mud during once-in-a-century storms. In other words, there is no guarantee that something will stay stable just because it's been stable for x years in the past.
You're describing temperatures hovering around freezing. One of the natural processes that leads to erosion is the situation where water, ice, or snow gets into cracks between rocks and then undergoes freeze-thaw cycles, expanding and contracting with each cycle. People quarrying rocks have sometimes used this effect intentionally to break rocks apart, e.g., by drilling holes in the rock and letting rain fill them.
The Trad Climber's Bible by John Long and Peter Croft has a brief section on climbing in the rain. They basically describe it as a misfortune that befalls you because the weather forecast was wrong, and they suggest common-sense ways of dealing with the emergency: don't panic; close your chalk bag and stick it under your clothing; slow down and be deliberate about your movements; place more gear than you normally would; pull on gear if necessary; avoid moss and slime.
