In The War Against Burrs...

I think you can shut off circulation to the tail bone. I never wrapped a tail but we used to use tail dock pads when we traveled with our smaller trailer. They were not suppose to be left on for long periods of time and not put on tight.
I think wrapping is only suppose to go as high as the tail bone. Again I never do it but it makes sense.
Here something I found here- 20 Tips for Tails @ Horse Tack Review
"Never wrap the top of your horse’s tail. It is nearly impossible to keep a wrap on a horse’s tailbone unless it is so tight that you run the risk of cutting off the circulation. Furthermore, if the wrap irritates your horse, it may actually encourage him to rub his tail."

Although it doesn't get all of them, I have a goat that thinks burrs are the best tasting food in the pasture and she does a pretty good job eating them as they grow. Might be something to look into, I'd never have a pasture without goats again. They really do help clean everything up.

Any particular breed of goat? My brother wanted a goat anyway...

Just stay away from Angoras. They are hairy and I can't imagine the burrs that would get in them. LOL.

My trainer had a student that wrapped her horses tailbone and the horse ended up losing his tail because the circulation was cut off. She doesn't like when I wrap Frida's because she says the tail helps the horse balance its movements. I'm also nevous her pasture mates will rip it off, so its just tons of show sheen, occasional MTG and a random comb once in a while...

Like I said it's really loose...I checked it yesterday and I could fit two fingers all the way until the tailbone ended. I won't wrap it that high next time. I was just trying to keep the mud off. But I will just wash it because it's getting muddy anyway... :p

Get some goats they love to eat Burrdock!

Th eonly problem I find is that you spend hours removing them and then the horses go searching for any plants that you may have missed. Our ponies deliberatly go finding them because they like the attention they get when you have to remove them

Prime sample
Daisy

I've been debating getting goats to help with the burr problem, but I know they can be bad about trying to escape. I've heard people suggest sheep to help with weeds and fence-lines. Does anyone know if they are helpful?

Sheep are grazers, not browsers; which is why goats are the ones you want for a burr problem. I don't have a single tumbleweed left in my goat's pen, but we have to seriously modify our pastures in order to make them safer for the goats; not only can they escape, but DOGS can get in!

I honestly don't worry so much about escaping goats, because they are such personable little critters, especially if you get one that has been socialized alot; all three of mine LOVE attention, and only one has been bottle fed. I worry more about neighborhood dogs that are running at large and looking for something to do...even though a goat will defend itself, it can't stand up for itself against a large dog or more than one.