Hi Karyn, Fencing is probably the most secure. Just make sure that the fencing is not weak enough that the dogs can climb it and bend the fence which can then be crawled over. Also make sure that the fencing is far enough out from the tree that if they weaken a place on the fence it won't fall in and knock down the tree. We have neighbors who are new to "country living" and kept planting trees in their pasture without any fencing around them. We wondered how many times they'd replant before putting fence up to protect the trees from the horses - third time was the charm!
Good luck! Lisa & Tempi (who prefers eatting bulbs more than trees) Bakersfield, CA