We have 2 boer goats that I have kept with my horses. They have never eaten my horses tails. A lot of people think that goats eat everything, but they actually are quite picky eaters. Goats are browsers, not grazers so they tend to do well with the horses on pasture as they eat more of the weeds down. And no they will not eat ALL your weeds. They will steal grain from the horses if they get the chance, so I would suggest having seperate feeding areas. Also you will want to have a good feeder, the goats will pee and poop in the hay. We made a homemade feeder with some scrap wood around the farm, i'll post a pic.
We keep them in a pasture that has split rail with horse box wire on the front, and electric on the rest of the pasture. The electric is 4 wire, only the top 3 wires are actually hooked up. They have NEVER escaped. We occasionally let them loose in the yard, ours are easy to catch, just shake a grain scoop and they come running!
I'd also suggest having 2 goats expecially if you will be taking the horse away riding/showing/etc. They don't like being alone and easily get stressed out.
Our goats are not aggressive and they are quite careful with their horns if you let them rub on you. I would NOT get a buck, they can be aggressive when they are in rut and smell.