To me, a well bred horse is when a good quality stallion is bred with a good quality mare, for a specific purpose.
When I say good quality, I mean of conformation which is fit for purpose, combined with a proven performance record, and a suitable temperament for the task at hand.
It is amazing how many people breed a their failure of a mare (unsound, unhinged, or both) with a quality stallion, and wonder why they get a youngster as similarly useless as the dam.
To me 'well bred' always has to be for the purpose... as you can have a well bred show cob as much as you can have a well bred racehorse, a well bred dressage horse or a well bred hunter. The absolute quality of conformation is not always as paramount as the traits of being tough, sound and willing.
For example, whoever bred Ferdie did a good job of producing an athletic allrounder who isn't a worldbeater, has some faults, but is ultimately a solid horse with a leg at each corner and a great brain. I wish I knew who his sire was... but he is the type of horse lots of people desire to have.
Whilst I am in favour of breeding being regulated more than it is, I still think their has to be an understanding that we need to breed all sorts of horses for all sorts of people and all sorts of job - so selection critera would have to be very varied!