<Fires up Memory Alpha and Wikipedia>
Ron Moore went to Cornell on a Navy ROTC scholarship and served on a navy frigate for one month during the summer after his freshman year.
Naren Shankar, another Cornell alum, got PhDs in physics and electrical engineering.
René Echevarria went to Duke University in North Carolina, majored in history, and also acted in theater.
Melinda Snodgrass went to college in New Mexico, has had a distinguished prose career both before and after TNG, and has degrees in both history and law.
Tracy Tormé is the son of Mel Tormé and also wrote for Saturday Night Live.
Hilary J. Bader studied mime in Paris and toured the U.S. for ten years performing a story theater play she'd co-written.
According to Robert Hewitt Wolfe, Peter Allen Fields (who wrote for TNG before moving on to DS9) lied about his age, joined the Marine Corps at 16, fought in Korea and was a P.O.W. He also had a career as a lawyer.
There were also a lot of veteran TOS writers who wrote on TNG in the early days, like D.C. Fontana, David Gerrold, John D.F. Black, who brought in their wealth of life experiences during the time they'd written for the show. There is more to life experience than just fighting in wars and having adventures.