It depends on what your 250's ratings are...
check here ;_ 2012 Ford Super Duty | View Towing Specifications | Ford.com
as depending on engine, 4x2 or 4x4, cab config, it differs... guessing max is 12400 ?
I would think a good wd hitch will handle the TT's weight distribution,
(FYI - dry weight is meaningless - use GVWR)
but the golf cart is all on the rear axles... what do you have maybe 6000 lbs rear GAWR
gross axle weight rating ?
my guess is that you will be over the rear GAWR or maybe the gcwr of your towing vehicle - only way to know is to weigh it at say a local CAT scale -> CAT Scale Locator | CAT Scale