In your area the colony will be broodless through the winter. In order to make a replacement queen the colony needs several things; a worker egg or larvae less than 2.5 days old, young nurse bees capable of producing royal jelly, pollen to fuel the royal jelly production. That's just to produce the queen cell(s). Next required is drones of a suitable age. Since drones take longer from egg to emergence plus add ten days to sexual maturity drone production will be required to start a minimum of two weeks prior to production of queen cells.
BTW, your SD colonies will have killed off the drones well before first frost.
Basically, in your area a dead queen in winter is a dead colony. Fortunately winter is the least stressful period for queens. The colony itself will do everything in its power, including self sacrifice, to ensure her survival. The beekeepers best course going into winter is to ensure the colony has ample resources in both bees and feed to allow them the best chance at survival.

And I will Add to Warriors "best chance of survival" during the winter months is a low mite count. About a zero chance up this far north with a load of mites.

Get the mites under control before fall to nil or they will kill your hive this winter. Many of us up here are treating NOW...and again with Oxalic before the cold sets in.