I just run the crappy incandesent lights that came on the trailer but I always disconnect them before backing down the ramp b/c cold water on hot glass results in a broken bulb most of the time.
Water trapped inside the lens will slosh up onto a hot bulb and crack the glass.
Yes, the sockets will corrode inside, when this happens I solder wires to my bulb terminals and feed them through the gutted socket. You can even solder a ground conductor to the bulbs base. The tension spring inside is particularly prone to corrosion, sometimes I just replace the spring.
There's all kinds of ways to get these old trailer lights working, salt is especially rough on them.
But there are nice waterproof ones out there that are pretty robust, it's just that I'm a penny pincher I guess. Yes, I've had about the same experiences you describe, it's easier fo me just to repair them b/c you never know when one gets smashed anyway.
Then there's the approach of finding a set someone else has tossed in the dumpster and repair them, I've done that as well.
