See if this helps
Trailer weights by trailer typesmall horse trailer sounds similar and would be 3,000lbs or more itself.
When I bought a camper the rule of thumb was to keep your towing weight down to 1,000 pounds less than its rated capacity.
Not knowing which particular model Tundra you have I looked up tow ratings for 4.6 Tundra and the minum listed was 6500 pounds. That should keep you within a safe margin.
You never said if you have a towing package with brakes or not. It makes all the difference.
I towed a heavy trailer with a pallet of wet grass 200+ miles with a simple bumper hitch, no trailer package or trailer brakes and don't wish that on anyone especially going to Colorado.
Just flat NO.
Not sure what an after market towing package might set you back but worth it even on a one time trip. I had one added eventually and was glad I did.
I was also glad the truck I owned was built with a transmission cooler.
