You have my deepest sympathy, these things are a real pest, even if the herbalists love them!
They come with their own natural silicon coating so cushing the stems'A BIT' isn't enough and any man handling must be done in the spring while they are still supple. Older ones are brittle and break easily into potentially rooting bits!
Time and patience are rquired, plus some rubber gloves and some woolie ones. Prepare a double strength bowlfull of your chosen weedkiller, preferably a one containing Glyphosate. THIS KILLS ANYTHING GREEN SO BE CAREFULL AROUND YOUR OTHER PLANTS. Don the rubber gloves and put the woolie ones over the top. Dip your hands in the weedkiller and crush each new horsetail between your soaked hands. As said, do this while they are still young and possibly more than once! A weekly chore but worth it to catch them as they emerge.
Everything previously said about the roots and hoeing is spot on. GOOD LUCK