In Animal Farm, how is Benjamin affected by The Battle of the Windmill and why is he so influenced?

There is no reference in the text as to how Benjamin was affected by the battle. We can assume, however, that he was probably less affected on an emotional level than any of the other animals. He had not always been quite as forthcoming  and seemed to be quite unaffected by events, as the following quote illustrates:

Old Benjamin, the donkey, seemed quite unchanged since the Rebellion. He did his work in the same slow obstinate way as he had done it in Jones's time, never shirking and never volunteering for extra work either. About the Rebellion and its results he would express no opinion. When asked whether he was not happier now that Jones was gone, he would say only "Donkeys live a long time. None of you has ever seen a dead donkey," and the others had to be content with this cryptic answer. 

This type of reaction was common of him. He had made the following comment before the battle when Frederick and his men were gathered around the windmill:

"I thought so," he said. "Do you not see what they are doing? In another moment they are going to pack blasting powder into that hole."

This remark indicates Benjamin's astute observation of what the humans were up to. He realized that they were planning to blow up the product of their extremely difficult labour. None of the other animals could see this. It indicates that Benjamin possessed a superior intellect, but that he was not willing to get involved and was quite apathetic to the detriment of his suffering comrades. Perhaps he believed that if he should strive to change things for the better, it would come to nothing as it had with Snowball, and he therefore remained aloof.

After their victory in this battle, it was Boxer, surprisingly, who asked what victory they were celebrating when the gun was fired, since the windmill had been completely destroyed. Squealer had taken exception to his remark and commented that their victory lay in the fact that they had driven the humans off an area which they (the humans) had just recently occupied. Boxer, who was injured and bleeding, then offered this cynical but remarkably accurate response:

"Then we have won back what we had before."

To which Squealer responded:

"That is our victory."

After this, there was a celebration and the animals solemnly buried their dead. Each animal was rewarded for his or her role in the victory with an apple, whilst the birds received two ounces of corn and the dogs three biscuits each. A few days after the battle, the pigs got drunk from a case of whiskey they had discovered and later decided to use a paddock to sow barley, for obvious reasons. Late one night, Squealer was discovered lying next to a broken ladder with a paint brush and a pot of paint not far away, next to the wall on which the commandments were written. The animals did not understand what all this meant, 'except old Benjamin, who nodded his muzzle with a knowing air, and seemed to understand, but would say nothing.'

Once again, it is obvious that he knew what was to come, for the next morning another commandment had been altered:

They had thought the Fifth Commandment was "No animal shall drink alcohol," but there were two words that they had forgotten. Actually the Commandment read: "No animal shall drink alcohol TO EXCESS."

This then, was the sum of Benjamin's responses to the Battle of the Windmill and the pigs' devious and self-indulgent actions.