Globe Artichokes - Overwintering

I had a nice first year growing some Artichoke plants and have cut them down for the winter. and covered them with fleece. However they seem to want to keep on sprouting new shoots. I am concerned about frost / ice damage as the growth as I have lost a couple of the fleeces from covering them.
Can anyone advise how hardy these plants are and what I can do about this new growth.

We planted some this year, and I dutifully chopped off the heads as they formed.

They look pretty down now, but I thought you just left them to regroup next year?

Ours are not well protected, so perhaps they'll die back on their own.

The RHS says

In cold areas, cover plants with a mulch of straw, compost or well-rotted manure in late autumn, to protect them during cold winter weather.

It's your decision whether you think your area counts as a cold one...

Another one who lets them get on with it. My 5 plants have been in place for about ten years now. Occasionally I chop a new shoot off and replant it in the spring, but otherwise nothing other than cutting down the woody stems. I'm sad enough to count the artichokes and can say that this year I had 132(!) They do take up quite a bit of room, but they look great and if any artichokes don't get picked the bees love them. Although I think towards the end of the season my neighbours used to hide when they saw me approaching.

First up why did you chop the tops off? Second even though I live in an area where a frost is not that regular one year we had -15C in early Feb when they were well grown and the artichokes wilted but they regrew to produce a crop. I really don't think they are that tender!

I think that they need to get established, Jambop, and the first year's growth isn't allowed to develop, so the plants get stronger below ground.

The 'flowers' we had this year were definitely not worth harvesting, and the ones we've seen close by were much bigger and worth a pick!

But there again, I've never grown these chaps before so will stand corrected!

Used to grow them when i was in Alton Hants.
Tell the truth i just let them get on with it apart from taking out the old stems.
Gurt big thistles that can look after themselves IMO.

Update. So as of end of February I have lost three of the plants due to rotting in the soil. I think this was due the very cold temperatures at the beginng of Feb freezing the the cut down stalks. It looks like I have 4 or 5 plants left that were better covered, so hopeful I will get some produce of them this year. Shame as they produced some really good globes last year in their first year. I grew them from seed in January last year and they were croping in the summer, so was really pleased, so not happy that I destroyed a good percentage of them! 

I will not be cutting down again based on this and what others here have said.

Artichoke are probably one of my favorite veg and definitely worth growing if you have room.