That is called RF interference and it is from the circuitry in the LED bulb, or the fixture the bulb is in. This depends on where the voltage regulator circuitry is that brings 12 volts down to 5 volts or whatever the LED voltage is. That really doesn't matter. Here is what will fix that in most cases. You will need to buy two of these for each light that makes the RF interference and maybe a couple more that will go on the TV. They come in a 2 pack. However I would experiment with one light first to be sure it works and you don't blow a bunch of moo-la. Snap-Together Toroid Choke Core-2-Pack - RadioShack.com
This device is called a Ferrite coil or better known as an RF Choke. It will filter out electrical noise in all sorts of places. With a little work and some luck it will stop that RF noise from the light. You are basically winding the power wire through this coil as many times as you can, and close to the light, but leave enough wire to help push the coil up in the hole and re-mount the light. Look at the picture in the link above. It shows a single wire but you should be able to use the double wire that has the negative and positive wire glued together. If it is too thick you can split the wire and use one coil on the positive wire and one coil on the negative wire. You might very well have to lengthen the wire to get enough through the coil to do the job. Start by trying one coil on a light. (or two coils if you split the wire) It may just stop it. The coil snaps open so you can wrap the wire around and around the coil until no more wire will fit and then snap it shut. If you have a long enough wire you are lucky and don't have to add any wire so there is no messing with connections, wire nuts etc. Hopefully there is enough room in the hole above your light to push the coil back up there. But there are also many variables in trailers and I have very limited experience in what is behind light that I can't tell you more. You can also put these coils on the other end of the wire after it comes out of your distribution panel but that is not the preferred way.
You can use these RF Chokes on the power cord on the TV as well as the antenna cable itself. It's a matter of just playing around with it.