I only remove the spent flower heads before I put mine to bed ! I would let the leaves die down naturally

yes I'd agree with that Grandmadge. The dead leaves often act as a winter protective.

Do agapanthus have to be over wintered in a greenhouse?

There's a beauty in one of my customers gardens which stays out doors all year with no protection ( on a light soil)

A.man, I leave mine outside but with a little protection, ie. in a corner under a shrub and a fleece on top!

I reckon you should buy it a woolly hat !

:)

Might knit one !!! Lol