In your area, overwintering in the ground is risky and survival depends on preventing the underground rhizome from freezing or sitting in water saturated soil. Hopefully, you provided enough mulch.
The brown dead stems are normal. You can choose to remove the mulch and see what happens. Better yet, lift the plant and check to see if the rhizomes have survived. It should not be soft or mushy. You can than replant the healthy rhizomes. Soil tempts are still cold and you are not likely to see much growth.

Kent

Thanks for the info.

I think I'll leave them because they're in a small bed and I may do more harm digging them up.

Should I remove some of the mulch to allow them air to breathe and grow or just leave it as is and they'll grow through?

One is coming up. Hoping the other follows suit soon