How do enviromental factors contribute to evolution by natural selection?

Environmental factors don't just contribute - they are the cause of the evolution of a species.

For example, the horse is descended from a dog-sized creature called the Eohippus, which had separate toes instead of hooves, etc.

It's evolution towards the horse came about through an environmental change of some sort. Presumably, the more jungle-like terrain the Eohippus would have thrived in began to thin out, becoming more open plains.

Without trees or bushes to hide in, the Eohippus would have been easier to prey on. The ability to outrun predators would have been favoured by natural selection over the ability to hide from them. As a result, the individual toes gradually became the hooves adapted to running very quickly that we can see today. The small organism would have evolved towards the powerful modern horse.

But without that environmental change, the Eohippus would still be here today.