I have a 2010 and had an AIP pump go under the 3/36K warranty. That was before they increased the warranty to whatever it is now. When the pump went, it didn't put me into limp mode. Took it to dealer, they replaced it by the next day and I was back in the truck and loving it.
As long as your payload is low enough, the Tundra is a GREAT truck to pull with. Plenty of power, plenty of brakes, transmission seems strong, rear end is plenty beefy. My father in law has a Chevy 2500 with the 6.0 and pulls an equal size trailer that is newer and lighter than my trailer. We both average about the same mileage towing and both trucks got up the mountains in central PA at the same speed (above the speed limit) and came down the other side the same speed just fine.
For an appropriately sized trailer, the Tundra is a great towing machine.