There are no herbicides allowed in organic production registered in Canada. Mature orchards tend to have few weed problems due to shading but weeds can be an issue in younger orchards.
Irrigation management, cultivation around the trees, mulching, and flaming are cultural controls used by both organic and conventional growers. There are times of the year when growth around the trees does not harm and can even be helpful. It is both possible and desirable to develop a tolerance for weed growth, or to even encourage certain beneficial species to grow around the tree.