No, you do NOT have to license the trailer, only the boat.
I HAVE registered my trailer, however… here’s why:
In WI it is not required, but it is in MN and most other states. If you travel to other states (or outside the country – ie. Canada or Mexico), and licensing is MANDATED in that state, the cops CAN pull you over. Once you are identified as a WI resident with a WI boat, you are okay.
However, why give them an excuse to mess with you… I go to Canada a couple times a year and to MN, IL fishing. A State trooper from IL and a Canadian Mounty BOTH gave me this advise.
Just thought I’d share! Hope this helps!