Ice sheet retreat:

An ice sheet will retreat at anywhere from 50 to 200 meters per year at the beginning of an interglacial period. That is not a large area for the members of the adjacent ecosystem to exploit. The trees drop seeds, the rodents carry them; the wind blows, the flowers advance. Ecosystems creep forward, like the jungle consuming a Mayan ruin. It's not just survival, it is also exploitation of new turf.

And while a glacier will scour to bedrock and deeper, what it leaves behind in the way of sand, gravel, till, loess, and rock flour contributes to some very fertile soil, especial at the margins; such as the Bread Belt of the Midwestern states. The poor drainage of the hummocky terraine accumulates organic material in swampy ecosystems. All of this is new frontier for species looking for new homes.

Much of what you describe with the rabbit's change in fur has to do with breeding, not speciation. I'll see if I can dig up some links on the efforts to domesticate foxes by the Russian fur industry. The idea was to domesticate foxes to make it easier to get fur. But what happened was that as the foxes were selected for less fear of humans, their fur changed color. The selection of genetic traits is multi-variable, and selecting for one trait will rusult in changes of other traits. But the species remains the same.

So how do new species arise? Well, one important driving force is isolation of ecosystems. Austrailia has marsupials instead of mammals because it split from the super continent at a different time than the other continents. Mountain ranges in Nevada, separated by hostile desert basins, have unique species of the same families.

But a bringing together ecosystems also creates speciation. We are experiencing that now as new invasive species are carried by human activity into new enviroments. If they are better at living in that envronment, they will take over the ecosystem. I get flyers all the time to pull weeds that are taking over the local grasslands. The Tamarisk Tree is taking over the river bottoms of the rivers of the Southwest US. New fish, birds, mussels, and insects that are new to North America in the last 500 creates a very long list. These plants and animals compete with the original occupants, resulting in new stresses and new selective forces.

But changes to ecosystems are not always the gradual process of glacial retreat or the even slower shifting of contients. They can be instant, from a local volcanic eruption to an planetary extinction event, and can render vast areas devoid of life. Yet, all that does is provide a new playground for the pioneers of life. The slopes of St. Helens are alive and growing and the rodent colonized the leftovers of the Cretaceous.