We used to tow a mid-size coleman/fleetwood tent trailer with Odyssey, back when Ody was new on the market.
I don't know what hitch weight our trailer was at the time, but, after one trip we *had* to upgrade to a weight-distributing hitch. It was mandatory for safety, the Ody's front wheels were pretty light with weight on the hitch.
From that point, the Ody had plenty of power, and adequate brakes. Eventually, that car went with my son to college for various forms of student abuse. Relevant here because we ended up having to put a new transmission in it, I always thought that was due to our towing.
Speaking for myself, I would not repeat the experience. It's hard to know if the tranny was up to it. Maybe it was. Lots of variables. I'm pretty sure that tent trailer was closer to 2000 lbs. The Ody was rated for 3000 or 3500.