I've got Geranium Macrorhizum living happily under a big hawthorn. Also cyclamen,(although they don't spread a lot). I've also go a hellebore in there which seems perfectly happy.

If you don't need to cover the ground all the time you could try some woodland plants which may be dormant later in the year like asarum, maianthemum, hepatica. Some ferns tolerate dry shade too.