Return of the Bur-icorn!

Somehow, despite my chopping off most of Annie's forelock into a stupid bowl haircut, she still manages to attract burs up there:

Just one this time-- the single "horn" of a bur-icorn!

I hate thistles, burdocks, thorns and wild grape-- and they love my pasture. It's hard to keep 'em down. Spraying with chemicals is obviously bad for the horses-- so that leaves mowing when possible, or digging stuff out by hand. You can imagine how well that works on 12 acres of rocky pasture. I've heard that spraying with vinegar will kill plants without harming horses-- has anyone tried it?