Caveat - I've never bothered with my own 2014 trailer which has conventional incandescent exterior lighting which seems to work well enough but I have read of some who've tried it and had all sorts of issues. :(
Vehicles these days are computer driven, many wired with CANBUS, which if designed to power incandescent lighting may not play well with LED circuitry. Although
this article refers to the problem with vehicles it could also be an issue with trailers as well since it's exterior lighting system is powered by the TV's electrical system. I'd use caution before proceeding with this project and wouldn't assume it's just a simple matter of swapping LED for incandescent. For some it may work, for others it may not, depending on the tow vehicle's electrical system. You sure wouldn't want to make this change and not only discover the trailer lights won't work but you've also perhaps somehow damaged your TV's electrical system. :E