Is it hard on a 7.3 l diesel to run only short trips around town?

Yes. Diesels are cold-running monsters that do not operate efficiently, until they are warmed-up. Short trips don't allow this, which is why you often see people idle their diesels for long periods rather than turn them off. I see this all the time in Texas, when people run into the store to shop. With their outstanding torque, diesels excel at hauling and towing. Short trips are best left for the family car.