This was a common problem with the TB’s of the last century and I will give you the solution that worked well with them and should work on any breed with this issue. It’s called “stabilization.” We’d spend weeks working on this until the horse would stay the same speed basically on a loose rein. It is described on EquestrianCoach.com in the video topic, Fundamentals Of Flatwork – Basic, and it has its own chapter within that topic called Stabilization. Watch that but I will give you the skinny.
First it takes patience, perseverance and time. Ask your horse to trot at a normal speed. Loosen the reins to a short loop by putting your hands and arms forward. Naturally your horse will speed up. As soon as he does, check him (take contact and increase contact as if you were going to walk and do not increase your leg) and use your voice (whoa). He will slow down to the original normal speed. Loosen the reins again and he will of course speed up. Repeat the check and voice command. It will take many, many hundreds of these to get the message across. Hopefully he is smart enough to get the message and you can proceed to the canter with the same procedure. Use the mildest snaffle suitable for your horses mouth.
Click here to view the video topic: Fundamentals of Flatwork – Basic
