Hi Simone, and welcome to permies! I haven't had to deal directly with horsetail, so I don't know how effective my suggestions will be for that stuff. But in general, the way I start a new bed over existing ground, whether it's pasture or "weeds," is to mow it short, lay cardboard or heavy paper over it, then cover with lots of woodchips. If the chips are already well into the decay stage I will sometimes plant directly into them, but usually I make a hole, put in a bit of
compost, and stick a plant or seed in there. This method saves a lot of digging work, keeps your soil life in good shape, and keeps down just about everything that gets covered (I still get the occasional dock or convolvulus shooting to the surface, and have to yank those out on my own).
You could do some parts this way, run the pigs on the remainder and follow with a cover crop, and see how the different areas fare.