Ajuga varietes have different leaves and different colored flowers but can become invasive and stays green/brown/red year round.

Here is a link that might be useful: Propagating Perennials

sweet woodruff might work for you. but the leaves tend to get a bit coarse as the year goes by. they flush small and bright green in the spring, with white flowers and grow larger over the season and darken to forest green about mid summer and stay green most of the winter, but by feb/march there isn't much left.

vinca might have a white blossom form but usually its purple

diggerb

Wild strawberry or Fragaria chiloensis or vesca would be a good choice. Tolerant of a huge range of climate and soil condtions, spreads well and produces white blossoms sporadically from spring to fall. Vinca minor 'Alba' is also a good choice but has a limited spring bloom, as does the sweet woodruff and the ajuga (and the white flowered form of ajuga is difficult to find).