Ugh. My boy did the same today. The easy quick and long term solution is to just roach (shave/cut) their mane. I LIKE my horse's mane though, so step 1 was to pick out any/all loose burs I could with my fingers, and step 2 was to use some sort of product (show sheen, mineral or coconut oil, really it's whatever you like) generously and slowly and painstakingly comb them out from the bottom up. Once it's bur-free, you can put a neck-hood or sleazy on, braid it, or just wait for them to go roll around in the burrs again and start all over. Sigh.