The relatively recent development of fair skinned homo sapiens living in Europe, and lactose digesting (milk consumption) enzymes in central Europe are prime examples. These mutations undoubtedly popped up occasionally long before they became useful to their owners. It was not until former Africans moved into Europe that they needed light skin to better use sun on the skin to produce vitamin D essential for good hip (reproductive) structure. Also, until homo sapiens began herding and milking cattle, there was no special utility to having lactose digesting enzymes. Once they had survival value, these genes proliferated rapidly by enhancing survival.
You have a provided an excellent example. Where I think it is a lot harder to comprehend the numbers working out on a completely random basis is in the origination of incredibly complex systems in species that did not have them resulting in an end state different from the one that provided the survival advantage along the way. So the feather mutation flourished because it provided warmth but that actually ended up leading to flight. And the numbers would seem more difficult with all the little bits and pieces that make up the eye but which until they come together to produce vision seem to have very little survival advantage.