Mine did exactly the same thing.
When I hooked the cable directly into the tv my picture was good.
When I hooked it up to the trailers input...garbage.
I removed the TV and them removed the panel behind it to get th the wiring.
(yours may be different)
I had access to both the amplifier circuit and the input from the trailer so I replaced it all....and it was still snowy.
Then I went to Radio Shack and bought a new splitter and that solved the problem. The stock splitter is a cheap piece of junk. I don't know why they couldn't spend 8$-10$ more when they built it. I would have paid for it!
Hope this helps.