Because horses are grazing animals, designed to travel long distances to find food and eat whenever they find it available, going for that grass is a perfectly natural behaviour.
As a first step, ensure your horse is getting enough forage (hay or grass) in her diet and that she has eaten before going out to ride. If her tummy is full, she’s less likely to be tempted to snack.
Next, work with her at home so that she consistently responds to your quiet leg and seat aids to go forward. A horse that is moving from her hindquarters can’t lower her head to grab grass as easily. Also, work on your riding position, ensuring you are balanced in your saddle, sitting tall and with your weight evenly over both seat bones. A well balanced rider is not so easily pulled forward out of the saddle.
Always pay attention to your horse and what’s available to her in the environment as you ride. When your focus is on your horse, you can feel subtle changes in her movement that signal where her focus is and what she is thinking about doing. The sooner you notice that she’s preparing to reach down for a bite of grass, the more pro-active you can be to prevent it.
As soon as you feel her move her head downward, immediately send her forward from your seat and leg. At the same time, close your fingers firmly on your reins (to create a block), pressing your knuckles into her neck if necessary so you don’t get pulled out of the saddle. Bridging your reins can also give you a stronger block to prevent her from pulling down. The more consistent you are with your aids and preventing the behaviour, the sooner she will stop doing it.
If you are re-training a horse that has been allowed to eat while being ridden, be prepared for her to try pulling down harder and refuse to move forward. It always takes more time to un-train an existing behaviour.
If you enjoy it when your horse has a ‘chew’ while you are taking a break during your ride, then teach her a cue that means ‘Okay, you can eat now.’ I do this by asking my horse to halt and stand quietly for a moment. Then, I release the reins and gently tap or stroke her shoulder or give her a voice cue. When it’s time to move on, I ask her to move forward from my seat and leg, taking up my reins again as she lifts her head.