I googled "solomon dougherty, franklin county, ky" and found a lot of hits, but I didn't go through them to sort fact from fiction. I think I tried "mordecai winter franklin county ky" also and didn't get much, but it is worth your time to try.
Look for histories of counties, biographical histories, and people who have already done the work
Look at 1790 - 1820 censuses for Doughtery and Winter. Count young males and females in the households.
Find out if the will book for Franklin County is online or still around somewhere. Also the record of deeds.
Find out where people came from who moved into Franklin County - migration paths. They probably came from Eastern Tennessee, <-- North Carolina <-- Virginia <-- Maryland or Pennsylvania <-- British Isles, or some similar path. You might find their families a little farther back up the path say 20 years earlier or so.
Look on rootsweb or ancestry message boards for the families in the locations. and rootsweb worldconnect.
If you get a hit on familysearch, see if it is attached to a person in a tree. But then use those trees only as a possible guide to the right ancestors. They, as well as trees elsewhere, are fiction sometimes.
In short, look everywhere and use google a lot. Someone has probably done these families and put the information somewhere.