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It's really rather simple.
All dogs in all public areas must be kept under control at all times. If your dog goes toward other people, it is not under control and must be kept on a leash, as others have said.
In my experience, the only dogs that are under control of accompanying humans without being on the leash are service dogs and other working dogs (such as guide dogs for the blind¹ (unlikely to find on a hiking trail, although I did once meet a blind hiker on a narrow hiking trail along a steep slope)) and hunting dogs. I've met plenty of hunting dogs in nature, and they all seemed to totally ignore me. I'm afraid of dogs (including Liams “sea sponge”), but I don't mind hunting dogs. They appear to be true professionals. And that's for the better, because keeping a hunting dog on a leash would be impractical. A hunting dog may startle me but as it ignores me it will not scare me.
For any other kind of dog, I have rarely if ever experienced that an owner was actually in control. Therefore, the advice in other answers applies: your dog must be on the leash at all times, because you almost never know for sure if other hikers are near.
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¹Of course, guide dogs for the blind are always on a very short "leash" (I don't know the correct word), I mean that I haven't seen that the human needed this "leash" to stop the dog from going to other people.

It's really rather simple: **All dogs in all public areas must be kept under control at all times.** If your dog goes toward other people, it is not under control and must be kept on a leash, as others have said.
In my experience, the only dogs that are under control of accompanying humans without being on the leash are service dogs and other working dogs such as guide dogs for the blind[^1][^2] and hunting dogs. I've met plenty of hunting dogs in nature, and they all seemed to totally ignore me. I'm afraid of dogs (including Liams “sea sponge”), but I don't mind hunting dogs. They appear to be true professionals. And that's for the better, because keeping a hunting dog on a leash would be impractical. A hunting dog may startle me, but as it ignores me it will not scare me.
For any other kind of dog, I have rarely—if ever—experienced that an owner was actually in control. Therefore, the advice in other answers applies: your dog must be on the leash at all times, because you almost never know for sure if other hikers are near.
[^1]: Of course, guide dogs for the blind are always on a very short "leash" (I don't know the correct word), I mean that I haven't seen that the human needed this "leash" to stop the dog from going to other people.
[^2]: Guide dogs for the blind are unlikely to be found on a hiking trail, although I did once meet a blind hiker on a narrow hiking trail along a steep slope.