I think it is either forgotten or, if the historian is interested in climate, it is placed at the forefront of any conclusions reached. It is then often dismissed as 'over the top' by some historians (sometimes probably with good reason). The difficulty lies in identifying how long any climatic change lasted and over how wide an area prior to estimating the effects it could have had.
(For example, it is the experience of Charles Dickens' childhood, with several winters of snow, that played a part in his concept of Christmas in, for (obvious example) 'A Christmas Carol'. This has allegedly affected the way anglophones in the 'West' have seen Christmas, hence all Christmas films and cards etc. tend to have snow. But was this a widespread phenomenon?)
It's the same with population and disease, especially in Late Antiquity. The population has first to be estimated, then the effects of the pandemic/endemic is estimated, and then it is put forward as a major reason for the Fall of the West. How accurate is this?