Dogs and cats have a totally different vision when compared to that of large farm animals like horses and cows.
Dogs and cats are carnivores coming from predatory animals through evolution while most farm animals, including horses and cows, are herbivores which are prey species. Maybe you are wondering what animals eating habits have to do with the way animals see the World. It has a lot to do and cats or dogs vision and visual system, in general, evolved to what is today thanks to the feeding needs and behavior of these animals during thousands of years of evolution.
The visual system is composed of the eyeball (with attachments like eyelids and tear glands), the optic nerves, internal connections inside the brain, and the visual cortex of the brain, located at the back of the head. There is no best or ideal visual system in animals but that serving the best to the specific survival strategy of a given species.
Predators (including casual predators like domesticated dogs and cats) require focusing their sight on usually fast-moving objects located ahead. To do this, the visual field of each individual eye overlaps with each other (when you close one eye you are left with the visual field of your other open eye). When both eye fields combine (left and right), this arrangement brings to life more vivid details of the object of interest (like a mouse trying to escape from a cat, for instance). This cooperation of both eyes to sharply focus frontal (ahead), far located (and usually moving) objects is called binocular vision. This kind of visual field integration is also present in us humans. Therefore, we also have binocular vision and use it to chase things or to detect danger ahead, for instance.
On the contrary, the visual fields of each individual eye in prey animals never overlap (like in domestic horses, cows, sheep, goats, and many others potentially “edible” to carnivores). Hence, these animals lack binocular vision. In compensation, they have very wide visual fields on each eye that allow them to spot close objects in a very panoramic way. Thus, they have a much broader field of vision than carnivores, allowing them to detect things at very lateral angles, even coming from behind. Predators like dogs and cats cannot definitely do this.
This way, a horse, for instance, can detect someone approaching from behind or laterally and start the best possible response for which he is best at: running!
Although prey animals are good at detecting visual changes in their surroundings (like for instance potential threats) located laterally, the not-overlapping of their visual fields creates a blind spot in front of their noses. Anything that moves in that space cannot be seen (which is weird for us humans to imagine). Dogs and cats (and us humans) can perfectly see objects moving in that area (and even further away) and will readily bite or scratch if menaced as this menace is rapidly detected by the highly accurate visual system. The menace reaction can be used to test the visual system in dogs.
Animals can perceive colors differently from us, but despite that, their visual system is perfectly adapted for their survival.