Hi Lauren thanks so much for the advice , it will help alot!
If your horse rushes, it means he's running away from you and your orders.
Be careful to be really gentle with him (especially in your hands, don't be too strong, this is usually why they rush, also look at your snaffle that may be too rough on him).
Try to ride him with no contact on the mouth and he will probably calm down by himself. When you feel like he's about to rush, pull strongly your reins and then drop it very fast (he will understand confort/inconfort).
If you can't control him, put him on a small circle and he will calm down if he doesn't want to fall ;)
Maybe you can lunge him before riding him? This way he will have less energy.
Hope I could help you :)