YOU DON'T need license tags for boat trailers in KY.
My current boat was originally bought in Tenn. (no tag required there, either) but the original owner did register the trailer. When my buddy bought it from the original owner & transferred the title to KY, he registered the trailer and got a license for it. When I bought it from him I just left it that way. I get the trailer reg/tax form in the mail about a month before I get the one for the boat.
Last year I went to the County Clerk's office to get the two combined .... and the clerk assured me that it was a done deal. Well, it ain't ... I got separate reg/tax forms again this year.