The animal has the right to be where it wants to be. In all probability the highway on which you were travelling was a forest long time back where the horse naturally resided. The construction of th highway has deprived the horse and innumerable other animals from their natural habitat. Something which we suffer when the Government or a private company acquires our property for construction of industries/factories/offices. We can go and file a suit before Courts for our property but unfortunately, the animals have no legal representation and thus we are free to do anything we want with their habitat.
Coming to the incident mentioned by you, fortunately for you we do not have stringent laws to protect the animals. We have the The Prevention of Cruelty to Animals Act of 1960 which was enacted with an objective of preventing infliction of unnecessary pain on animals. Under this Act, you can be charged for Cruelty against animals under Section 11. Sadly, there is no option of imprisonment for this and the amount of fine is only Rs. 100. Besides this, you can also be charged under Section 428 and 429 of the Indian Penal Code. Under these provisions it is illegal to maim or injure any animal and the accused can be imprisoned for a maximum of 5 years and can be asked to pay a fine. Here again, a complaint has to be made to the Police and will have to be substantiated with evidences and witnesses to prove the charge.
The fact that you were driving with your DL in an insured vehicle will be of no consequence if you hurt an animal or a human on the road.