Is this asking a woman to cheat! If she'd like to join me down at the beach on Friday?

Deceit is what makes cheating. If she can relay this invitation to her husband, and if she’d be okay (hypothetically) in the reverse situation, say her husband were going to a nude beach with another woman, then with the element of deceit missing, it’s not cheating.

If deceit is involved, it wouldn’t be wise of you to be. I’d say tread carefully. Decades ago I lost a friend killed by a woman’s jealous husband. The friend had told me that he and the woman were only friends, and I believed it, but she was using him to try and stir up her husband. It worked too well.