Gradualism vs. Punctuationalism
If I understand your question correctly, you are essentially distinguishing between the timescale on which the variation in the character of interest is generated, and the timescale on which selection prunes the population based upon that variation. The argument is then that "all the evolving happened gradually, long before the selection event" because that is when the variation was generated. 

To me, this seems to be a misuse of the term "evolution", which is usually defined as a change in trait or allele frequencies in a population over time. Under that definition, much of the evolution does occur via the selection event. Before, you have a wide range of trait values; after, only a narrow selected set of trait values. In such a model, selection indeed is the major cause of allele frequency or trait value change. 

In practice, both processes are usually acting in concert; variation is being produced by mutation and recombination and eliminated by selection at comparable rates so that the net amount of variation in the population is at an approximate steady state. This is essentially the model Darwin espouses, though note that Darwin does not have our modern understanding of heredity and therefore is not able to explain how variation is generated or preserved. 

Additional note: When thinking about models of the kind that you describe, it is also key to understand that if you have a large number of loci affecting your trait (e.g. coat thickness), then the Gaussian distribution prior to strong selection will not include the extreme phenotypic values. If there are 20 diploid loci interacting additively to determine coat thickness and the mean individual has 20 thickness alleles and 20 thinness alleles, no individuals in a reasonably sized population will initially have all 40 thickness alleles, or even 39 or 38 etc. Selection for thickness will change the mean, and will also result in individuals outside of the initial range of variation. If the mean is 30, you may well get an individual with 38 or 39 or even all 40 thickness alleles. So once selection occurs, new more extreme phenotypes will suddenly appear. Nothing strange has happened in terms of rates of generating new variation; in fact this is just a consequence of reassorting the current alleles under the new allele frequencies.