We too took a new plot this year and it's riddled with horsetail. I spent many days during the winter (while unemployed, which gave me the now rare opportunity to spend lots of time up there) weeding and turning the soil. Next winter set yourself the hard but very worthwhile task of getting as many roots as possible out. It'll be very very very boring and possibly back breaking as well, but the more roots you can get out then the better.
From now until then, just get every shoot you see as soon as you see it. The idea is that if you repeatedly remove shoots and as much of their root as possible you will eventually exhaust it. Beware: the root is very brittle and will break easily, so excavate around it as much as possible and pull carefully.
Also pay attention to the edge of your plot: we're gradually building a new fence around ours and taking great care to remove clusters that have been allowed to establish themselves there. In our case the root systems are well established under neighbouring paved pathways between the plots, and horsetail has a remarkable energy for putting up green shoots very rapidly. Encourage neighbouring plot holders to also attack it, because it if charges ahead in the plot next door it'll soon enough be back in yours.
I'm suspicious of any weedkiller solution... you just have to keep hoeing it on a regular basis. You will get there, but I'm afraid it's not likely to be completely gone for a couple of years.