I had privet with no ill effects to horses. They are suitable for laying. I have heard stories that it is toxic but have failed to find any evidence of that, or the toxic substance responsible. It grows like weeds around here.
Years ago, the wild privet hedge that existed when we moved here had declined. It was thin on the bottom, top heavy and a lot of the hedge was thick trunks with lots of air seen through it.
Then the neighbour's cows wandered through it, so that was the trigger. I'm British from a long time ago, so decided to layer the hedge. The stumps got sawn out, the younger, slimmer stems cut and layered horizontally against the ground, weaving in and out and slanting sideways, as per picture.
Very soon these young stems had rooted in many spots and the hedge thickened up wonderfully and has been clipped into a very nice, thick hedge.