I wear my watch all day and only take it off at bed time. It's waterproof, so I even wear it swimming. For me it is fun to see when I take it off how tan I am. It's really my only tan line. I would be afraid of getting really sun burnt there if I ever took it off outside since it has never seen the sun except on rare occasions and it really white.
I have three tan lines... under my Apple Watch, under my wedding ring, and under the sandals straps on the tops of my feet! And the last two are fainter since I do take the wedding ring off if we will be on the beach so I don't lose it in the sand and the sandals come off when I'm lying by the pool or on the beach.
Like anything else, if there's utility behind it then it gets worn.
Nudist or not, if its crazy cold my ass is covering up. It doesn't make me less of a nudist, it just means I'm cold and using whatever I can to warm up.
Watch is no different, especially a smart watch. If it has utility, then wear it. As far as I'm concerned, nudism isn't just an obsession with OMG WEAR NOOOOOTHING OR ELSE. Nudism is the understanding that clothing has utility but shouldn't be required. Just like I wear layers to stay warm, I'll wear nothing to cool off.
At least that's my take.