I have a 2014 Ford F150 4x4 STX with a 126" wheel base, 3.7L V6 FFV engine,trailer sway control,elec 6-speed auto trans w/tow mode, 3.73 ratio limited slip axle, 6650 GVWR package.
Just wondering if it can handle a 4 horse stock trailer hauling approx 2400 lbs of horses?

 

Your regular cab 3.7 w/3.73 axle and 4x4 has a GCWR of 11,500lbs. That translates to a max tow weight of 6300lbs for your truck. Assuming the trailer is about 1000lbs, it'll pull it but don't expect to break any land speed records. While the 3.7 is a great engine, it doesn't have a ton of torque. Make sure to keep the transmission in the tow mode so the engine can turn the rpms up.

 

2014 Ford towing guide

 

Which confirms the 6300# figure. However, you may exceed the truck GVWR and/or rear GAWR if the tongue is heavy and/or you have heavy cargo in the bed.