You can get very high wire fencing which no-one can climb over (with tightly strung mesh so that they can't go through either). My friend has some round his horse's field - they are showjumpers and one of them is prone to sailing over anything less than 5 feet). I'd say its about 7 feet in height. Does cost a bit but its not an absolute fortune, and you get gates made in a similar fashion.
Whereas if they went in with what I personally think is a rather noveau riche attitude towards owning land and barked at everyone they saw, they'd probably spend more time worrying about their horses, rather than the villagers looking out for them and enjoying their paths round the field. Theres a woman near me who has recently moved into a house with a few acres, and there is a public path running through it, but she invariably comes out shrieking and yelling that she is going to call the police. So obvious that she isn't used to owning land and is still in the "I'm so important now I've got land camp". Its only a few acres after all, not an ornamental walled Georgian garden with a full-time gardner tending it.
Also I know a lot of horse people who have post and wire fencing with a string of electric tape run as the top strand, again to keep the horses in but almost impossible to climb over or through. Looks very smart too.
Does your land look disused? You say you have 7 acres but its not clear if you do anything with it, and if it looks sort of disused, people will be more likely to use it as a shortcut.
It doesn't seem that you have a very big problem with people on your land, but something about this interloper disturbed you and he is perhaps distinct from somone taking a one-off shortcut or getting lost on a walk.