How about the 40's in Gainesville at the Fairgrounds.
My uncle, Ben Parks, and his brother, Roy, used to keep horses at the stables at the old Fairgrounds. I can barely remember around 1944 - 1946 (I was about 5 years old) going to the track with my dad and watching the races and seeing the horses that Uncle Ben and Roy raced. I don't remember if they actually raced themselves or they had a driver to race their horses. I do remember one time getting to sit in someone's lap in the sulky and take a lap around the track. I think I have a picture of me in the sulky that day.
If the track in Dawson County you refer to was in the bottoms on the Chestatee River it was at least fairly close to land owned by my Great uncle Charlie Martin. Probably Ben & Roy Parks raced in Dawson as well as Gainesville. I think I know someone who might remember the Dawson County track as a boy and the racing there in the 30's. I will contact him and let you know.