I am looking for a groundcover suitable for my front yard under a Silver birch on either side of a dry Japanese style rock stream. Garden is facing east and gets only morning sun. The ground cover should not grow too high as I do not want it to hide the spreading junipers that are already planted.
This sounds like a lovely almost Japanese style front yard. As you have rather shady conditions and do not want a groundcover that grows too high I suggest you look at the following possible options, which all do well in shade, average, well drained soil, and are winter hardy in Toronto. Wild ginger and foamflower are native plants.
Wild ginger (Asarum canadense) spreads slowly and is low growing (height about 6″ -12″) . It has nice downy, heart shaped leaves and brown flowers that are hidden under the leaves
Foamflower (Tiarella cordifolia) has 3-5 lobed leaves that make a pretty ground cover and the fluffy white flowers on long stems are a welcome sight in May
Japanese spurge (Pachysandra terminalis) grows to about 8-12″ and also comes with variegated leaves. It can be slow to establish.
Barrenwort (Epimedium) species and cultivars come with different attractive leaves and flower colours. Epimediums grow 8-15″ tall and have very delicate leaves and flowers.
Although they may grow taller than you like, Maidenhair fern (Adiantum pedatum) and Siberian bugloss (Brunnera macrophylla) could also be of interest.