Unless you have a very high ranking horse you have to match the top skill of the horse with the main skill needed for the competition. The only comp with speed as a main skill is barrels so your horses are unlikely to see any rosette comps.

To have a good chance of winning rosettes currently a horse needs to be born from 100 blup parents to get maximum inborn skills. Ideally they should have a genetic potential over 31000 for most breeds and should have beach rides done to transfer skill to the main one from the lowest.

They then need to be in an EC offering bonuses of 40 in each skill and you need to give them the best tack possible and all the store bonuses.

It is not easy but it does feel good when you win the first rosette.