First, do you have a Check Engine light on? I'd guess not, since you didn't mention it. Where are you located?
My first suggestion is to check to see if there are any diagnostic/ trouble codes. Some will not turn the Check Engine light on, but most will. AutoZone/ Advance Auto/ etc can not check the codes on a PowerStroke truck. It does use a standard OBD 2 connector, but different programming. A regular code reader will not work. You'll need either a high- end Snap On, Mac, etc scan tool, or the Auto Engenuity software to check codes.
Since you didn't mention a CEL (Check Engine Light), my next suggestion is to replace your CPS (Cam Position Sensor). It costs about $30.00 from a Ford dealer, and will cause issues very similar to what you described. Ford actually issued a recall on them a few years back. They're a known problem on the 7.3 liter trucks, and have been since the engine was introduced in late 1994.
If the above items don't help, check your fuel pump. The 7.3 will run with a failed fuel pump, but you will have fuel delivery issues under a heavy load, such as pulling a trailer up a hill. One the passenger's side of the fuel filter bowl, there's a yellow lever. Open it, then have someone turn the key on. In addition to hearing the pump running, you should see a steady flow of fuel out from under the truck. The yellow lever is a fuel bowl (where the filter is) drain.
The issue could also be caused by a bad UVCH (Under Valve Cover Harness). They feed power to your fuel injectors, and the connectors on them occasionally short out or wires burn through.
Your issue sounds like a fuel supply problem, if it only happens when going up hill. Have you tried it under a heavier load (bigger trailer?) on flat ground?
If you're around Nashville, TN I've got the software to pull the codes on your truck and would be glad to try and help you sort this out. :thumbsup: et us know what you find.