I have been gardening lately. We use a bit of Permaculture, some Bio-dynamics and potter with what we like. We have 6 and 1/2 acres here, which was not cared for all that much prior to our moving here, although you can see at some stage someone started to make some lovely gardens.
I don't use chemicals at all on my gardens, with the proviso that the manure that comes from the horse, probably has some chemicals. This is because the grains used to form her feedstuffs were probably sprayed at some stage. But we don't add to this.
We have added tons of manure to our gardens, we had two horses here for over three years, and even now, her ladyship has about six to nine per day. I will not go into the digestive processes of horses here.
Now there are some advocates within the organics "movement" who do not feel that companion animals and horses are useful animals. Okay you mostly do not eat your cats and dogs, nor do we traditionally eat horses. In many places in the world they do, and with relish.
However, I think these animals are as useful as any dual purpose cow or chicken any day. I do not feel cows nor chickens are very useful as watch animals yet cats, dogs and horses are excellent early warning systems. They have exceptional hearing and sense of smell. They also have quite obvious body languages if you care to take the time to learn these for your particular animals.
Horse manure in the quantities even one horse produces it in is a valuable organic resource. Horses are also capable of providing traction - useful for larger scale organisations. Horses, being single hoofed animals are also very good for treading organic waste, such as pulled weeds, partially composted leaves etc, into the soil - both when it is wet and when it is dry.
I guess this would be also applicable to donkeys.
Horses also reproduce themselves and can provide milk if required. Their milk is quite sweet although not as nourishing to humans as cows milk is. Tartars make it into yoghurt, cheese and ferment it as well.
I am also of the opinion that dog, cat and horse fur (hair) can be used in weaving and felted cloth. All animals develop a thick warm winter coat of considerable length and as it sheds can be collected and incorporated into threads. Main and tail hair is quite strong and can be used to enhance rope fibres and some other uses that nylon can be put to.
Cats and smaller dogs are excellent mousers. They can also be encouraged to eliminate feral birds, for example, sparrows. If you go to all the trouble to grow food and then put it buy, you do not want your storage area raided by foraging rodents. Mouse traps are not all that useful with large numbers of mice. The smaller and medium dogs can be effective rabbit hunters. You can either use the rabbit bodies for feed - yourself or your animals - or dispose of the corpses. Rabbits are not a welcome animal anywhere because of the environmental damage they do. Most dogs love to hunt.
Dogs of any size can be effective deterrents for intruders. They do not necessarily have to attack people, but appearing quite ferocious can be very helpful. A really determined bad person isn't going to let a dog of any kind impede whatever bad they are going to do, but a novice or nuisance person can be deterred by a ferocious appearing dog.
Dogs are also useful for getting their owners out doing exercise.
So people who do not think these types of animals have a place in organic systems really should think again about their usefulness. Just because we choose not to eat them as well.