The '11 def stayed in 6th gear easier when pulling, my trailer weighs around what your horse trailer weighs. Probably closer to 6000 with water and all the stuff inside it. I should pull on a scale one day to find out for sure. It's about 5300 empty if I'm not mistaken, it's on the sticker right?
I bet you'd be surprised if you put it on a scale.
Our trailer is supposed to be 3,500 lbs empty, and was over 7,000 loaded when I weighed it. Granted, we had 750 lbs of motorcycles in the back, but that means there was still over 2,500 lbs of other stuff in there. And yes, all of the tanks were empty.
Propane tanks, propane, optional air conditioning, pots, pans, dishes, cutlery, food, cans of pop, beer, clothes, towels, lawn chairs, kids' bikes, barbecue, dog food, etc., etc... None of that stuff is included in the trailer empty weight spec. and it adds up fast.