Depends on the plant - if its hydrangea, best left on.

Can you tell us which particular plants you have inind, Peking? For example, I leave the hydrangea heads on until spring, but I cut back most of the perennials after they finish flowering unless I want to collect seed.

There are definitely some perennial plants that need the top growth left on to give a little protection in the winter - e.g. Penstemons.

So - we really need to know which plant you're asking about, Peking.

Thanks for comments - I omitted to name the plant in question. Hence modified question

I always dead head my agapanthus then leave it to rest for the winter in a sheltered corner.

I leave them until the stems go brown, then take them off. They're in the border, not in pots.

I cut the stems off,when its finished flowering...(pot grown)..and as it's a tender one,it will be wrapped in fleece,when the leaves have died down,and kept in the shed..