Yes and F150 will tow a horse trailer but that's not where the issue lies.
-Stopping is just as important as go power, F150 will have smaller brakes then an F250/F350.
That's false, F150's have different brakes for different models, some are the same or better than some F250 brakes. You can't make blanket statements of what a F150 or 250 can do or can't do, both come equiped differently.
That's like saying a blue truck has better brakes than a red truck.
Besides horse trailers have brakes on the trailer axels, that's what stops your trailer, and it is vehicle weight that stops it as a backup. The weight difference between a properly equipped F150 and a base 250 is negligible.
There is alot of overlap in capabilities, My 2004 F150 had a light duty, 3:31 axel, smaller brakes, 16" wheels, and a dinky 4.6 engine that was only rated for about 3500 lbs if I remeber, with a small horse trailer it couldnt get out of it's own way. But it got 22mpg interstate,,,
My current truck is a 2007 F150 with a 5..4 High output, FX4, Max tow package,huge brakes, will run circles around the 250 gas trucks, heavy suspension, and rated at 9800lbs towing. Will pull a 3600lb sundowner gooseneck with no issues, stops fine, plenty of weight.
But I get 18 highway empty and 14 towing.
My point is I wouldnt listen to anyone that makes blanket statements about 150, 250 ,350, look at the manufacturers tow guide rating of the exact model and features of the specific trucks you are comparing.