Did Richard Nixon have a “nap hour” while he was president of the United States?

Yes. He didn’t admit to it, but he’d block off time in his calendar in the Eisenhower Executive Office Building, away from the White House, where he’d spend time thinking. Some of that thinking did indeed involve him having his eyes closed and snoring.

Here’s the first three links I find from Google Books:

• Pat and Dick
• Being Nixon
• The Psychedelic Sixties: A Social History of the United States, 1960-69