WHILE FACETIMING us from London’s Heathrow airport, Arnold Schwarzenegger sipped from a pink tea set he called “cutsey wootsy.” But even when he’s equipped with delicate accessories, there’s nothing dainty about the imposing bodybuilder turned film star turned governor.

Now 72, he first became obsessed with exercise when he realized he could jump up and grab a thick tree branch near his childhood home in Austria. “I became a fanatic because I could do, like, three chin-ups the first time I held on to it,” he said. “Then my...