Winter sowing is mostly useful for plants that have cold dormancies like Penstemons. All subtropical species do not need it. If you want to experiment, make sure you have plenty of seed for a normal resowing later in the spring.

I have never tried to winter sow Agastaches. You didn't mention what species of Agastache you were attempting to grow - many of them, especially the western hummingbird types probably aren't hardy in Chicago and that fact is important if you are trying to get your plants to flower the first year. From my experience Agastaches need to be started very early if they are to reach decent flowering size. This past winter Agastache cana was sown on New Year's Day and tranplanted into cell packs in February. It made a big difference since seedlings grow very slowly under lights and on the porch, taking months to reach a safe outdoor planting size. You could make cuttings now of favored plants and winter them indoors. This may or may not work. Agastaches for me have always been much more difficult than salvias to winter over indoors.

I've done them under grow lights over the winter in cool rooms, but they prefer cool, sunny greenhouses with just a bit of water, since they are mostly dormant.

Agastache rupestris is hardy in USDA zone 5. Having probably originated in warmer climates, most of the new forms are probably not so hardy. Those from the Denver area probably will be hardy to zone 5.

I agree, Rupestris might be the best one to try, I've known several zone 5 folks who have had multi year success. A friend in zone 4 had good survival with herbacious perennials like Salvia darcyi and guaranitica by tarping his bed and then storing bags full of fall leaves on the tarp. It gave him around 3 extra zones of protection. It would probably work with Agastaches since it kept the soil dry.

Yes, quite a few Agastaches are list as zone 5 but I would suspect they need perfect winter conditions like a rare winter drought.