Hi paulcoco,
Welcome to the Heartland Owners Forum.
A BH 3160 EL has a GVWR of 15,500 lbs. The F250 probably has enough horizontal pulling power, but it might come up short on payload. For planning purposes, you should assume 20% of the GVWR will rest on the hitch, or about 3,100 lbs. Add to that the weight of the hitch, bed liner, bed cover, tools, firewood, pets and passengers. You could need around 4,000 lbs. of payload capacity.
The truck should have a label inside the driver's door showing payload capacity. If less than 4,000 lbs., you should look into getting an F350.
You can get more information from
Fifth Wheel St.