Thanks for writing. Horsetail can be a tough weed to get rid of. Vinegar alone is not strong enough to control the weed (though boiling water should cause sufficient damage to the foliage).
Are there other plants growing with it? If not, you can try solarizing the soil --- or cutting everything in the area down to the ground, tilling or working the soil a bit, then covering it with clear plastic. Be sure the plastic is anchored down and the edges are "sealed." Over the course of a couple of months, enough heat should build up underneath that it kills the horsetail (as well as a lot of the weed seeds in the soil).
Alternatively, you can try treating the horsetail with an herbicide if it's allowed in your area. The safest route would be to apply the herbicide with a paintbrush directly on the horsetail; that way you don't spray and get more product than necessary into the environment.
---Justin, Senior Garden Editor, BHG.com