Not quite clear on the registered breed statement. I don't believe there is such a list since, most horses will do ok with proper training and handling. There are some general requirements though. If you want to find out what breeds are more likely to do well in an event then do this.
Take any horse and run it through all the trial events. Take note on what the Big/small breed bonus is for each event to find the horse types which will do best in that event. Types not listed at the bottom will not perform and would be unsuitable for a commercial brood operation.
Once you have the types, take note of the highest %'s stated in the trial notes for each event. That is the stat titles you would be interested in. Then you can look through the BC list, and there is an area sorted by type, to find specific horses whose BC suits that particular event.
http://ebilmoose.com/vhr/wiki/pmwiki.ph ... ListByTypeExample: Barrel Racing
Big bonus- stock
Small bonus -pony
Important stats
health always important
surefoot 10 %
movement 0 %
strength 12 % speed 14 % endurance 6 % intellegence 0 %
Hyperness 3 %
Horses that do well for this would be Stock horses with high stat titles of Speed and Strength, with endurance coming in 3rd most important.
Some suitable horses that are seen fairly commonly.
ApQH
Ph/S/
Ph/Eg
AQH
Am/Eg/
Am/Eg
ACL
Ph/Ex/
Am/Ex
Also check the current and completed events regularly to see what people are using. Many many horses with lower stat titles than those above do spectacularly for their owners but may not be suitable for a commercial brood program (will not get used much). I am just guessing that you may be interested in public brooding's so if not then go for whatever breed you happen to like at the time.