This is most likely rabbit damage.  Woodchuck is a less likely culprit.  The chewing is a bit atypical of a rabbit--but perhaps it chewed several times over weeks or months.  

Yes, a smaller wire mesh screen such as chicken wire added to the bottom will generally do the trick.  An even smaller mesh will help to prevent mouse damage to the base of the tree.   If the damage is more than approximately 40% of the circumference of the trunk, the tree is probably not worth trying to save.