Wow... there's a challenge, low growing, flowering ground covers for zone 3!
I love the idea of mixed "lawn" and having flowers in it.
Cold season grasses for lawns are usually fescue and ryegrass. Native grass for you would include blue grama, various sedges including pennsylvania sedge, oatgrass
Here's some little low growing flowers that grow well mixed in with lawns and that should be cold hardy for you:
Field pussytoes antennaria negelecta, baby blue eyes Nemophilia menziesii, or the related Five Spot
Nemophila maculata, Crimson Clover Trifolium incarnatum or other clovers such as strawberry clover, Forget-me-Not Myosotis sylvatica, Johnny Jump-up Viola cornuta and other wild violets, Sweet Alyssum Lobularia maritima, virginia strawberry Fragaria virginica, roman chamomile chamaemelum nobilis, elfin thyme Thymus praecox 'Elfin', English Daisy Bellis perennis
I'm thinking what you would want to do is make up your own seed mix with some grass seed flower seeds of whatever of these flowers you can find. Fall is a good time to plant grass seed.
If you don't want to DIY it:
Here's a company that sells various seed mixes of grass and low flowers:
You would need to contact them to see if their mixes would be cold hardy enough for you
Prairie moon nursery https://www.prairiemoon.com/
sells a variety of seed mixes, for lawn alternatives, native grasses, ground covers, different situations of dry/wet sun/shade etc. They have some prairie seed mix for upper midwest USA, which ought to be kind of similar climate. Again you would need to contact them about your specific climate and what you are trying to do, but I'm sure they could help.
You probably need to know these people also:
Hope this helps!