Enjoy your new truck, but realize its limitations and work within them - You can find a minimal camping shell that only has beds and storage. I have owned trucks that I modified over their lifetime to carry or tow more comfortably and safely but eventually upgraded when needs/wants surpassed what I could upgrade. Don't let these guys with endless deep pockets of someone else's money scare you off with their comments about replacing your Tundra.
Hint: Since you need as much payload as possible available to you, consider packing things in water tight containers that can be carried in or on the horse trailer instead of in the truck. I bet you can easily transfer 200-300 lbs of gear, clothing and food to the trailer (my enclosed trailer is my catch all for bulky or heavy items).