I have nothing against archery range competitions... but I don′t think Skyrim is the right setting. It would have been perfect in Oblivion but perhaps axe/hammer-throwing competitions are more Skyrim style, or feats of strength. And yes I know Nords != viking but can you honestly imagine Nords as the archers of legend ? Better save archery competitions for if we ever get a TES game that happens in Valenwood, granted bone/metal arrows may not be the thing for everyone (they don′t allow wooden arrows).
what about vikining funerals? They shot flaming arrows at the corpses as the drifted far away. I'm pretty sure that the archers would be pretty good or else the body would just drift off into the ocean unburning, and that would just be embarrassing.
What i mean to say though is that bows and arrows were pretty much a major tool of war everywhere in the world. If an army with bows and arrows went against an army with just throwing axes the army with throwing axes would most certainly lose mainly because of the much shorter range.