How might environment cause a DNA change/mutation in the structure of an organism?

From necsi.edu, the following quoted words have been written about the evolution of a white-haired rabbit population surviving over a brown-haired rabbit:

"1. There are hares living in a cold, snowy, polar region. All of the hares are brown* and many of them are killed and eaten by other animals each year, so more are born than survive.

2. These hares are competing for life and struggling to survive, partly by trying to avoid predators, to "not be the one who gets eaten."

3. Each hare is a little bit different from other hares, but one time a few hares are born albino, white, because of a mutation in the genes.

4. This variation in color helps the albino hares to survive. Against the white snow, predators have a harder time seeing them, so more of the albino hares are able to survive and therefore to reproduce.

5. In the next generation there are more white hares, because the white hair gene is passed on. In this generation, too, more white hares survive and reproduce. They pass the albino trait on to their offspring, who also survive and reproduce more than do the brown hares. Gradually, there are more and more white hares in the population, until the entire population is made of white hares."

...Now, the survival of white-haired rabbits makes sense in a primarily "white" colored environment.

What I've questioned were other mutations which have been said to occur. One example, dawn horse, a.k.a. "hyracotherium." Many years ago, a very small horse was believed to have existed with fingers instead of hooves, and a very, very small stature. Over time, people believed the dawn horse grew accustomed to rocky terrain (I can assume), and eventually (after a long process) fingers had been replaced with hooves, and fingers had been lost (not to mention diet possibly affected the size of "hyracotherium's" family in future time.)

A question remains, "How might a DNA mutation have occurred if (unlike the albino, white haired rabbit) "hyracotherium's" relatives began to change because of physical surroundings?" Would a person assume DNA to have a "mind" capable of choosing to change because of harsh conditions. How can fingers disappear at one point, and hooves be a replacement? (Understanding finger-loss to have occurred over many, many years...and "hoof formation" to have developed over many, many years also.)

What are your opinions/beliefs? Theological discussion would interest me, along with what else I could hear.