The old couple are very minor characters in Harvest Moon 64.
They are not residents of Flowerbud Village and only show up only during festivals. They come to watch the horse and dog races.
Once you win your first horse race, they will come to your farm one day to see your horse again and say that it's beautiful. At the dog races, they mention they have a dog named Baron who they would like to enter in the competition, but they never do.