That's interesting, because here in the UK our archery clubs are basically built around doing just that. We have roving and field archery competitions as standard here, where distances are unmarked and natural terrain such as hills, valleys, fences, water and so on make up the courses, a bit like in golf!
There are no real limitations in draw weight at these competitions, although I think the British Longbow Society puts a 70lb upper limit on the bows. No sight marks allowed of course. This means that there are many archers in the country shooting incredibly accurately (I'm talking tiny kill zones on 3d targets such as the head of a duck for example) at any distance with fairly heavy bows. Once you hit 70lbs and feel like going up, the EWBS take over, where true medieval bows are only allowed, with a 70lb minimum weight. Again, the events at the EWBS included roving, unmarked distances, wand shooting and so on. The only real difference is that the bows have to be exact replicas of Mary Rose bows, with the same construction and profile.