Your post is probably going to get very different reactions depending on what country people are from, since bicycle infrastructure varies.

In the US a "cycle path" would probably refer to a multi-use path. Dogs are allowed on most multi-use paths in the US. On a multi-use path with cyclists and pedestrians, cyclists must yield to pedestrians. I assume that means their (leashed) dogs as well.

Now, dog owners who walk their dogs off-leash on a multi-use path with bikes and clearly posted leash requirements? They can go fuck allll the way off. Because the last thing I need in my day is a fucking terrier throwing itself in front of my bike wheel.

In Europe and other places I'd guess that "cycle path" might mean a bike lane that is painted on the sidewalk where bikes have priority? If that's what you're talking about then I agree dog owners should not be walking their dogs in what amounts to a traffic lane, but there's also not much you can do about it other than sound your bell/horn or steer around.

Shitty dog owners are shitty. Not much to be done except yell at them to be less careless of their dog's and other people's safety. And on the other hand, don't be a shitty cyclist and bully pedestrians if they have the right of way.