For as long as I can remember (about 40 years), boat trailer lights have always been difficult to maintain and rarely do they work... UNTIL NOW! Our trailers feature L.E.D lights that are completely sealed and submersible. That means the corrosion and cold water / hot light bulb issue has officially been eliminated. If you have an older trailer read on...
Make sure anytime you add, remove or replace a trailer light be sure to make a water tight solid connection. Plain old crimp butt connectors just won't cut it on a boat trailer... wire nuts are the WORST! Try to either solder your connections and apply liquid electrical tape of use heat shrink butt connectors and apply liquid electric taper over that. That is the best way to "keep connected".
UP THE ANTI
If your lights are cracked, corroded or loosely sealed, spend a few extra dollars and invest in L.E.D replacement lights. They will last 3 or 4 times longer than incandescent bulb lights and require zero maintenance.
Always unplug your trailer lights from the vehicle before backing down the ramp. Hot bulbs and cold water doesn't mix.