I too have those burrs in one of my pastures, and when my horses start coming in from that pasture with burrs in their manes and tails, I clear them out while they eat and do mane and tail checks at every feeding while they have acess to that pasture. By checking and taking out at every feeding, I only have small amounts to take out.
To get the burrs out, if a big clump, I break up the clump into smaller clumps. Then I pull the hair out of the clump, not out of the horse. Maybe 10 strands at a time until the burr is only caught in a few strands and can be finger combed out. Then repeat until all burrs are out. I lose very little mane and tail hair this way.
If the mane and tail is really packed full, you may need to soak the mane and tail in baby oil or some other product that will make the hair slippery. Then break the clumps up and work the burrs out. Though if the it is really matted and tangled, your only choice may be to cut everything off and let it grow out, and resolve to catch it when there are only a few burrs at a time and not let it get that bad again.
Good luck.
Spotted Pony