Whether your counter conditioning or training behavior, value matters. The more difficult the task, the higher value the reinforcement needs to be. You wouldn't work a really difficult job you don't enjoy unless you were getting paid big bucks - horses won't either. The more the horse dislikes the task, the more physically or emotionally difficult the task is, the stronger reinforcement we need to match it.
If your horse lovessss to go fast and play, you need to put your reinforcement on slowing down, stopping and relaxed. If your horse is a slowpoke who conserves their energy, you put your reinforcement on movement and activity and effort. The harder the skill is for your individual, the more reinforcement needs to be there to match it.
This doesn't mean you have to pull out the sugar cookies! While this can help in some situations (like then the vet is actually doing something sucky) its not a good place to practice in that level of arousal or excitement or desperation for the reinforcement.
Instead reduce the value of the task, so your low value reinforcer matches it. If trotting is reallllyyyy hard, just ask for the speedy walk and stop to reinforce with your regular reinforcer. What ends up happening is you build a history of reinforcement and begin to classically condition the hard thing to be more fun and easier, more valuable. So as the desire to do the hard thing increases you can ask for more between reinforcements. Using reinforcement history of a stimulus or behavior to help build it up, slow and steady. Rather than putting two high value extremes against each other - which creates conflict.