You could plant a selection of early flowering bulbs at the foot of the hedge, and if you beef up the soil a bit you could add things like Bergenia and Hellebores, (unless it is relentlessly sunny) to give you something to look at through winter. I find that I don't mind the bare look too much until January and by then you could already be looking at snowdrop flowers
With some caution, how about ivy? Wonderful wildlife plant for winter. Controllable on your side by cutting runners when they come over the stone wall. It will climb through pretty much anything and doesn't need pruning in the conventional sense. Your neighbour may have some concerns though, depending whose hedge it is.
Irises, reticulata and unguicularis types both flower in winter (or very early spring) and like dry, poor soils so may love that situation, depending what the hedge is
Gardening on the edge of Exmoor, in Devon
“It's still magic even if you know how it's done.”
For the difficult conditions (dry, probably lacking in nutrients and at least part shaded) I would recommend Vinca minor (lesser periwinkle.) This is more a trailer than a climber but will grow almost anywhere and will sprawl through the bottom of the hedge, especially if that has 'bare legs.' Evergreen and flowers on-and-off most of the year, more so in the spring.
A trowel in the hand is worth a thousand lost under a bush.
The main problems are likely to be that the ground in the 6" border will be full of hedge roots, when the hedge starts growing (assuming it's not Leylandii or something else that doesn't regrow from brown wood) it will probably easily cover that 6 inches, and access will be needed to cut the hedge in summer/autumn.
Spring bulbs and tough stuff like Vinca are good ideas but won't cover the whole front of the hedge (and that's spring interest not summer).
I can't think of any plants that would cover the bare hedge for this winter but not interfere with its regrowth and cutting later on. Maybe large evergreens in tubs standing on top of the wall, if it's sheltered enough that they wouldn't blow off, you can reach to water them now and again, and budget will allow?
Doncaster, South Yorkshire. Soil type: sandy, well-drained
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Irises, reticulata and unguicularis types both flower in winter (or very early spring) and like dry, poor soils so may love that situation, depending what the hedge is
“It's still magic even if you know how it's done.”