Weeding and seeding
See https://extension.umn.edu/lawns-and-landscapes/lawn-care for information on both. It provides a link to this care calendar https://extension.umn.edu/planting-and-growing-guides/lawn-care-calendar.
Use the weed killer now. Make sure you are selecting the correct one for your weeds.
See http://apps.extension.umn.edu/garden/diagnose/weed/ for help in identifying and eradicating the weeds.
Seeding can be done in late October or early November. See https://extension.umn.edu/lawncare/dormant-seeding Make sure to check the label of any weed killer you use to make sure that it does not conflict with the seeding timing.
This is a great response, complete with economical answers and helpful links, which I possibly could have found for myself but am grateful in this case not to have had to journey through the jungle of information to find just what I need. The weather has turned to such an extent that NOW I am wondering whether it is—too soon—too late to seed!
I would still wait a week or two if possible. As the last link states, it is best if you can time it so that the seed is spread shortly before a snowfall that stays on the ground. That is not always possible, but you want to seed when it won't get warm again and encourage the seeds to sprout.