Yeah, you definitely want some nice winter tires, and an all-season is no good substitute for that. I lived in Michigan for most of my driving life and owned all AWD cars in Michigan, and don't even think AWD is an appropriate substitute for good winter tires. It's certainly a nice-to-have on top of winter tires though
If you're leasing for a few years, I think it makes sense to get a set of winter tires. Even if they were only lightly used, I'm sure you can sell them off at the end. Risking sliding around and damaging your car (or worse) due to poor traction is not really worth it if you live in a winter climate.