you are right it is a kind of Horsetail. It's the Common or Field Horsetail (Equisetum arvense). It spreads by rhizomes underground and is an extremely difficult plant to get rid of. There may be chemical treatments that might work or you could just keep manually pulling it all until you exhaust the undergound reserves. Siomilarly covering the whole area with black polythene or some other light excluder for a year or two might work.