This is a tricky question to answer in full confidence. No matter how you look at it, different people react differently in a panic situation.
If the animal is small then just drive on straight…….sad but true, it is the animal welfare or you and your occupants welfare….what is more important at that point? Think about it. You steer to avoid a small animal and end up in a ditch or worse, you hit an oncoming car.
If it a large animal, then you need to avoid it by braking and steering away, deciding quickly if the animal is not going to bolt in the direction that you are steering towards to avoid it. This is a situation that calls for quick judgement.
For me, I will brake hard and head dead center into the animal if there is traffic on my right and if there is no room on my left to steer safely towards.
I have personally hit a cow once on a village road. There was a motorcyclist with his family and a car behind him and on my right was a village coffee shop with people around it. Hitting the cow damaged my car and injured the cow……..but no lives were injured and more importantly no children were hurt. I paid for the cow to compensate the owner and managed to drive my damaged car to my body-shop for work to be done.