ok, first of all, carolina jessamine isn't jasmine at all. and yes it is poisonous. second, i have loads of it, and the only problem with it is if someone mistakes it for honeysuckle (hard to do if you know that honeysuckle has a fragrance, carolina jessamine doesn't). then, if they try to drink the nectar, it is poisonous. third, i prefer to let mine grow up into my trees
so it is out of reach, but i can still enjoy it.
as for planting it on a fence, i see it around horse and cow pastures here all the time, in pine trees
and i've never seen a horse, cow, or goat nibble it.