Hi Worried Neighbor, thanks for using Ask Extension.

There is a good chance your rosemary is just stressed, not dead.  The dull green leaves is typical of snow exposure and/or sudden temperature change. Rosemary is cold hardy down to ~20°.  Some varieties are better than others. Check branch viability with a scratch test by gently scratching the bark on a stem. If the tissue underneath is green and moist, the plant is still alive. Brown and brittle, or mushy indicates a non-viable area.  If the stems remain firm and green, the plant can recover. Prune lightly to remove dead material 

You can either allow semi dormancy and place in a cool garage with some light
(40–55°F) or without light, you should grow inside.  If you have a nice southerly facing window where your plant can get a minimum of six hours of sun, that would be ideal or you can supplement with a good grow light. Rosemary does not like soggy soil so make sure you water deeply and allow the top inch of soil to dry before watering again.  Good air circulation will help keep prevent powdery mildew. 

If the roots and main stems are unharmed your rosemary plant has a good chance of overcoming its bout with the cold.    You may lose some leaves and stems, but they may not signal the end.  Look for new shoots in the spring.

Rosemary: The herb with winter problems - Gardening in Michigan

I hope this helps.