This is a great thread, I wonder if the moderators would sticky it? We frequently get these questions about tow vehicles.
When I was doing a lot of hauling with a 16' stock trailer, I had a 3/4 ton gasoline with the full towing package including the transmission oil cooler and it was great. I went all over the state in the rig, over Afton Mt. Repeatedly and to horse shows most every weekend with no problem.
I now have a two horse steel trailer, and only haul locally to trail ride. A gasoline Dodge Ram 1500 is fine for this, but I will tell you, with two large horses on the trailer, we're slow. Safe, but slow. I would not take this rig fully loaded into the mountains, or on hauls longer than an hour. It's fine for my needs now, but if I start hauling longer distances, I'll go back to the 3/4 ton.
The concerns about hauling with an SUV are 1.) wheelbase 2.) stopping power 3.) wear and tear on the transmission and 4.) engine size - in that order. Wheel base smaller than the trailer and stopping power can be deadly - literally. Hauling with an SUV absolutely can be done, but you must be very careful with the match of the vehicle to the trailer. I hauled a 16' stock with a V8 Jeep Cherokee with the tow package a couple of times, and you had to be very, very careful how you loaded the trailer, or it would jerk the tow vehicle all over the road. With most of the weight in front of the axles, it did okay, but not a rig I would choose, but any stretch of the imagination.
Anybody who hauls anything with anything without the trailer brakes hooked up to the controller is asking for trouble, period. The electronic brake controller is not optional equipment, IMO.