add playlist from Apple Music to iPod nano

If you mean the subscription service which Apple has named as Apple Music, then you cannot add music from the Apple Music subscription service to an iPod nano.

If you mean adding the music that you have purchased (from any source; CD, Amazon, the iTunes Store etc.) by using Apple Music the programme that is replacing iTunes, that is possible.

No idea why Apple would give two distinctly different things (an application or programme that handles music that you've purchased, and Apple Music (the subscription service) where one pays for monthly access to Apple's copy of music, the same name.