Well then, where to begin?
Horses have spent far, far more time running around on grass and various other natural surfaces than on synthetic ones, so don’t automatically assume an artificial surface is better than grass to ride on.
The going, or footing, will depend on the amount of moisture there is in the ground. That is the simple answer. The more the moisture the deeper the going. Bone dry concrete = hard -> saturated mud = heavy, sometimes heading on to bottomless, as found hunting in Ireland. However, the moisture is combined with endless variables such as sub-soil, drainage, season, wind conditions, time of day, management practices, type of grass or blend of synthetic material, and so on.
As a rough guide, when walking on a good turf surface one should feel a slight cushioning underfoot, almost a little bounce. If a horse moves over good grass there should be little evidence of an imprint. As the ground gets wetter, obviously it becomes muddier. Horses usually don’t mind mud very much, unlike humans. As the ground gets wetter the hoof prints become more obvious, deeper, and the sward will start to cut up if the horse is moving at speed. The wetter the ground, the deeper the hooves go in and the more effort the horse has to make to lift its feet. That is why deep ground can pull off shoes and pull tendons and ligaments. By contrast, hard ground has no spring to it: it can feel dead underfoot. Then percussion causes jarring and damage to tendons and ligaments but at least the shoes usually stay on.
Other surfaces, e.g. sand, bark or specialist synthetic riding surfaces, should also provide that slight spring and cushioning. Too hard, too deep will be detrimental to the horse. Unfortunately, it then gets more complex because one has to take into account the way the horse moves its limbs and feet, the slide and slip, the speed, the grip of the hoof as it expends and contracts - which all happens naturally on grass because that is what horses evolved to run on - however, the science behind equestrian surfaces is increasing all the time. Even on non-turf surfaces, the footing still depends on material, moisture, time of day, season, management practices. Similar to turf, good footing in e.g. a showjumping ring should have that bounce and resilience and the best surfaces don’t show much of a cut, so that hoof prints are almost invisible.
Managing turf takes some knowledge and not every climate or environment can provide good grass so synthetic surfaces are ever more popular. They are level, consistent, relatively easy to maintain and stand up to a lot of use. Unfortunately for the horse, there is increasing evidence to suggest that horses need to work on a variety of surfaces in order to support and maintain soundness.