Hi Herb Woman. I was faced with a similar situation at my allotment plot when I took it on three and a half years ago. I followed Charles advice and mulched with manure and then 800 grade black polythene. I chose to leave my mulch in place for two full seasons as the horsetail was so well established; I dug and cropped about a third of my plot whilst this mulching took place. I am now cropping most of my plot and, although there is some regrowth, the horsetail and bind weed is so weak that it easy to remove with regular trowel patrols during their growing season. This has kept up my morale whilst I learnt about growing and was a long-term solution to a rather tricky situation.
I hope this helps.