What happens after an advantageous mutation

In the short term, the fate of any mutation (however advantageous) probably depends on luck as much as anything else. If the slightly fluffy individual happened to be eaten by a predator before it reached sexual maturity, or failed to find a mate, the mutation would be lost. If the individual did manage to survive and reproduce, the mutation might start to spread throughout the population. The extent to which it spread would be determined by a combination of chance ("genetic drift") and functionality - if the slightly fluffy members of the population were more resistant to cold, and cold was sometimes a threat, they would be statistically more likely to survive. Slight fluffiness might then become typical of the species.

Subsequently, a mutation for enhanced fluffiness might appear and spread through the population in the same way, conferring a shaggier appearance, a greater degree of insulation, and therefore improved chances of survival even relative to the slightly fluffy individuals. In fact, a mutation influencing the size of an existing structure is probably more likely to appear than a mutation altering the basic form of a structure (e.g. converting scales into slight fluff), so once the fluff had appeared it would be quite likely to become thicker, longer and more widespread on the body if insulation was important. Fluffiness-enhancing mutations could readily accumulate over many generations, until the fluff was truly impressive.

The fossil record tells us that the most primitive feathers seen in the avian lineage were indeed quite "fluffy" - they were filamentous structures that would have looked more like the downy feathers of a modern chick than the stiff, blade-like flight feathers of a fully grown modern bird. Getting from filamentous feathers to blade-like ones is a significant evolutionary step, but one could imagine a couple of possible pathways. Perhaps filaments that were somewhat stiff and organised into vaguely blade-like shapes (the "blade" being formed by multiple individual filaments, analogous to the barbs of a modern feather) had a rudimentary aerodynamic function, or perhaps such structures were better for visual display (a possible function even of filamentous feathers, depending on their colour). Once stiffness and a blade-like form had appeared, by virtue of another mutation, they could be refined in the same way that a slightly fluffy dinosaur could become more fluffy.

This is just a hypothetical story, though it's informed by some real evidence from the fossil record about how feathers evolved. The story might seem unreasonable in that it invokes one mutation after another, but mutations (changes in the DNA sequence) are actually quite common in evolution - it's just that most of them have little or no phenotypic effect or are downright detrimental. Mutations that result in advantageous traits such as (in the context of the example I've outlined) slight fluffiness, enhanced fluffiness or stiffer and more blade-like feathers are rare in the grand scheme of things, but given a large number of reproducing individuals and a large amount of time they do occur and can spread through the population with the help of natural selection. The power of this mechanism is that, once an advantageous trait is in place, it can be built upon by subsequent cycles of mutation and selection. Hopefully this hypothetical example provides a sense of how a new phenotype might indeed "grow in scope" and eventually lead to novel functional possibilities.