There are a few ferns that will tolerate a dry position and my memory is letting me down re the best variety, sorry! For winter colour try the evergreen euonymus fortunii, several good varieties to choose from and all take kindly to clipping to keep them the shape and size you want. Daffodils and snowdrops would be happy, and the dry summer conditions may well suit the pretty little iris reticulata which hate to be wet in their dormant season. There should be enough sun for sedums which don't mind dry ground though they may not like the drip from the tree leaves.
Retaining moisture is best done with the addition of humus, eg good home made compost, but as a last resort gel crystals dug in below the surface will work quite well - best used at the bottom of planting holes and mixed well in before adding the plant. Hardy fuchsias are worth trying but you would need the gel as they need moisture.
Some of the low growing cistus might be OK, again if they survive the drip, and good old perennial geraniums are reliable and many are long or repeat flowering.

Many thanks for your helpful information, I am very grateful and hope to implement some of your suggestions.