Perennials like trees die best when sprayed in late summer-early fall, when they are moving food reserves out of the leaves into the stems, roots or bulbs. Often spring sprays won't kill due to the plants pushing those nutrients out to the developing leaves.
A pre-emergent soil herbicide such as Surflan can prevent new seeds from germinating when applied in the winter- early spring, it won't harm established plants, -check the label for that- and gives you plenty of time to get it applied over the months of winter.
