When John Andrew retired at age 65, he wanted to spend more time skiing, a hobby he had picked up in his 40s. His son gave him a book listing all of the ski resorts in North America at the time—some 700 in all. Looking at the book gave Mr. Andrew a wild idea: Why not ski every single one of them?

“I figured having a goal would keep me out of the rocking chair,” says Mr. Andrew, now 84.

And...