There will be times when everything is going right that they'll just sit there and let the good strides roll. But they will always be aware of each stride, allowing each correct stride, and be ready to influence the next stride in order to achieve the shape they want and play the game they want. All this directed attention is hard work. A lot of people don't understand how mentally intense even what looks like simple groundwork can be for both the handler and the horse. That's why you never make a baby horse's early work sessions very long.
Some horses can only take a few minutes in the very beginning.
They have to work up to a longer attention span. When you start them under saddle, you may have to shorten their work sessions again and work them back up to more time. Every horse will be different. When things start to go wrong in a training session, it's usually because the trainer had a lapse of attention. They took their attention off the horse so the horse's attention wandered, too.