Most F150 size and smaller trucks have a receiver rated for 500lbs of tongue weight, or 1000lbs of tongue weight using a WDH.
You need to look at the specs of the truck you are considering.
A 4000lb trailer, is that the "dry" weight or the GVWR?
If the GVWR is 4000lbs, you could conceivably have a 600lb tongue weight (15%), which would necessitate the use of a WDH. Trailers in this range are generally single-axle units with high tongue weights to allow the use of a single 3500lb axle.
If the dry weight is 4000lbs, your trailer will probably end up in the 5000-6000lb range loaded and ready to camp, and will most certainly have a tongue weight exceeding 500lbs, again necessitating a WDH.
In both cases, this is assuming a typical F150 type truck or smaller with a typical receiver with a weight carrying limit of 500lbs tongue weight.