Hi! me again. Reread some of these responses. Thinking back... and something you should consider also, I just remembered:
A 12 horse riding lawn mower would have enough power to move a travel trailer, as far as the engine goes. But the transmission and drive assembly is a different matter. That was the problem with my riding mower when we purchased our first camper after the pop-up. The engine ran fine, but the transmission couldn't pull it. The "belt" drive simply wasn't strong enough. The transmission just slipped and the trailer went no where.
I now have a John Deere 700 series, hydraulic everything, (nice machine and cost more than my car!) It would pull, but the support for the hitch ball is flimsy as soft tin and won't support the weight of the trailer tongue. If I use a wheel under the trailer tongue jack, the trailer coupler is too high. Just something to think about.
Good luck!