Im thinking of re starting a Shield sword nord, but is it annoying fighting dragons that wont land if you don't invest in archery or magic?
For PURE Melee fighters, it can be annoying, unless you invest in items that help your frost and fire resistance. In the case of a Nord, you'll really only need to invest in fire resistance, as your inherent frost resistance is good enough for most of the lower level dragons.
Basically, with dragons, a pure melee fighter needs to wait it out and use shouts against the dragons until they get frustrated and land. THEY will land eventually, especially if they can't really damage you with their frost/fire breath.
Then you move in and wail on 'em.