You do know you can lock horses up within a field don't you ... by locking the gates to the field? I'm surprised you haven't seen locked gates to fields before ! You live and learn I guess.
No you can’t lock them up in the way you describe.
Clearly, you know absolutely nothing about horses because if you did you would know that in order to care for them properly, their owner has to go in and out of their field quite a few times a day to attend to water, cleanliness of tanks or buckets, food, poo picking, rugs or fly masks depending on season, vet and general hoof and welfare checks, and the horses themselves if in work will be led in and out the field regularly and maybe twice a day if they come in at night, and finally, machines such as mini tractors have to be driven in and out to top the fields or harrow them or re-sow etc in order to look after the land properly and attend to solid and electric fencing.
Also, horses themselves, being prey animals, like to have a clear view out of their own fields across adjoining land.
Also, we the owners like to have a clear view of the horses from outside the fences in, so that we can observe the horses from outside their enclosures every time we pass by.
Finally, the field in which horses live, has to be able to be accessed quickly and speedily in case of injury or illness within the herd.
Therefore if horses were kept in conditions similar to Fort Knox, with multiple locks on eight foot high doors, surrounded by eight foot high solid fences, they could not be looked after appropriately.
Sure, we can padlock a gate and put up signs, and turn electric fencing on, and increasingly owners are installing solar powered security cameras, but as pp have already said, passing members of the public sit their dc on gates, allow them to swing on gates, jump gates and generally do not respect gates, despite gates being expensive to buy, install and maintain.
I hope that’s clear enough to understand?