I was born in Far East Russia not far from the North Korean border and I regularly visit Yanbian, the "third Korea" right by the North Korean border in China, so I know a bit about the climate in that region. Much like Northeast China or South Korea, I think the best time to visit is in April or early May. The weather should be very pleasant during that time of year.

Winter is cold in North Korea but it's relatively short. It usually doesn't get properly cold until at least November, but I've lived in Russia, Scotland and Canada so take my opinion with a grain of salt.