looking after artichokes

[yellow van]

Hallo. I inherited some globe artichokes on my plot but don't really know how to look after them through winter. This year's growth is dying off now, going yellowy and brown spotty, and arties left on are doing that thistle thing, but there is also about a foot of geen new growth coming out of the bottom. Do i cut this new growth down to protect it from frost, or leave it and use fleece to cover it? Or dig it up and put it in the grrenhouse? TIA