For anyone trying to erect a living willow barrier against
deer: I recommend planting with one of the species of willow that are deer-deterrent. Salix purpurea and Salix triandra cultivars in particular, plus maybe hybrids of these species. Among the many cultivars available, for a narrow fedge you might also choose ones that tend to grow unbranched. Otherwise, I know cultivars differ for reasons of branch thickness (basket weaving), new branch coloring (create a winter rainbow!), pussy willow showiness, vigorousness (Fish Creek is especially fast growing; maybe
enough to weave a living bridge), and other various traits. (If you're going to make a barrier, or weave a bridge for that matter, it's nice when you think it looks good!)
Also, when making fence/fedges against deer, it seems important to have width and not just height. One suggestion (that I intend to use) is to run two lines of fedge, about 2' apart, to keep them from wanting to jump the distance. (If they might get caught in it somehow, they're not going to want to jump it!) But with that plan, perhaps only the outer line need actually be resistant to their foraging... and the inner line could be entirely showy willows (corkscrew versions? pussy willows?), or a different kind of plant altogether! Because it's there for thickness of the barrier, but not as the outer line of defense. So pick something you'll enjoy.
Also, the recommended distance between willow rods being planted as a deer deterrent fedge, so as to keep the little ones from pushing through: is 1 foot apart. Sounds to me that once something like this was established (and it's not a little thing to do!), one could be selling or gifting willow rods to their neighbors every year thereafter, for their own living barriers. Sometimes it pays to carefully pick out the specific cultivar(s) you want to use (and then wait patiently for probably years while it all establishes enough to give you the full distance of rods you need to plant). But once you've got it, this could be another form of income security. Just food for thought!