Q.Can you propose all weather plants/flowers that will prosper in a shady area – two trees overhead – all year long without removal or
replanting during the winter period? Temperature may fall to minus 10 during the winter.
You have several issues to contend with. Tree roots are #1. If you are planting under the canopy, you will encounter tree roots. It isn't a good idea to damage these; contrary to popular opinion, most trees have feeder roots only in the top 8 inches of soil. Big roots that go deeper help to anchor the plant but do not nourish it. So tree roots will pull moisture from the soil potentially leaving your plants to wither. Is anything growing there now? Next is shade; there is dappled sun/shade with filtered light reaching the plants and deep dark shade where little will grow. Are perennials that die to the ground in winter OK or are you looking for evergreens? Attached are two links with plants that will tolerate the cold and do OK in shade. https://www.gardeningknowhow.com/garden-how-to/gardening-by-zone/zone-5/zone-5-shade-plants.htm
https://www.prairiemoon.com/search.html?Search=zone+3+#/filter:ss_usda_zones_facet:Zone$25203/filter:sun_exposure:Shade/filter:ss_usda_zones_facet:Zone$25205
