The animals in the other farms react in a mixed way. At first Mr. Pilkington and Mr. Frederick, the owners of the adjacent farms, are very worried that the rebellion would spread. There is some evidence that this would happen as other animals learned the song "Beasts of England." What made this situation even scarier is that the animals began to sing it. The implication is that there will be a rebellion.

When Mr. Pilkington and Mr. Frederick come to understand the situation, they counter any potential rebellion by spreading rumors that the situation on the farm was horrible. The animals, in other words, were not faring well at all. They said that the situation was dire. It seems that most of the animals believed them, as they did not revolt. 

However, a few animals did try to help. For example, when Mr. Pilkington and Mr. Frederick began to march to attack the farm, pigeons flew over to Snowball and Napoleon to warn them about the attack. This is why the animals were prepared. 

In conclusion, most animals wanted to revolt, but a mass revolt did not happen.

In Animal Farm, how do the neighboring farms react to the animal revolution?

When the Animal Farm begins to show that it can be productive without human control, the neighboring farms begin to feel threatened by its mere existence; this is magnified by the propaganda spread by the pigeons, who brings tales of freedom from oppression to the animals in the surrounding areas. Farmer Jones begins to spread dissent, complaining that he was never a bad master of the animals, and the others farms join with him to overpower the animals and take the farm back.

Nevertheless, they were both thoroughly frightened by the rebellion on Animal Farm, and very anxious to prevent their own animals from learning too much about it. At first they pretended to laugh to scorn the idea of animals managing a farm for themselves.
[...]
Jones and all his men, with half a dozen others from Foxwood and Pinchfield, had entered the five-barred gate and were coming up the cart-track that led to the farm. They were all carrying sticks, except Jones, who was marching ahead with a gun in his hands. Obviously they were going to attempt the recapture of the farm.
(Orwell, Animal Farm, george-orwell.com)

Their reaction is based in fear, since the success of Animal Farm would throw their own control into question; after all, if the farms do not need humans in charge, what purpose do the humans serve?The easy conversion of animals from willing subordinates to rebellion is beyond their understanding; in their minds, the animals are merely acting out a fantasy that is doomed to fail, but they become more and more worried as the song "Beast of England" spreads among their own animals. In an attempt to restore their status quo, the humans attack the farm, and are repelled; Snowball leads a triumphant counterattack that routs the humans.