Creating a map of Koppen climate zones for a very Earth-like world is quite easy, with the right instructions. However, what if the climate is several degrees cooler? Do I simply shift all the climates equator-ward, or is it more complex than that? If not, how much should I squish them?
Ice Age Climate
Climates and Geography
While there are situations where shifting equator-ward (and colder climates shift downward with altitude too remember) may not be the precisely right answer, that is generally the case so long as you remember a few points
colder weather may change currents that would bring different weather fronts which would change temperature in specific regions (Europe is warmed by mid-Atlantic current for its latitude. If Ice Age shifted that current Europe would be much colder even if the average temperatures elsewhere were less shifted). Currents are also shaped by the continents around which they move water.
shifting rain bands make different areas deserts that get much hotter especially with the right types of soils and bedrocks (see shifting rain bands and the Sahara moving north and south in Africa)
the koppen system fixates on latitude/elevation, precipitation levels, season where majority of precipitation is received, summer temperatures, etc. Other systems for classifying climates exist, focus on other factors in varying emphasis and leave out others. Different models have different strengths and weaknesses and the science as a whole is not fully grasped as the factors that could effect this system seem to still perplex the people predicting the weather.
- science here will change as we improve our knowledge. Fixating on accuracy in arbitrary circumstances such as providing accurate climate maps with this world will make the work more quickly dated. Quality content within the setting while leaving the setting more ambiguous such as mentioning of the Ice Age without Koppen acronym might be a better approach for the narrative happening within it.
There are a lot more examples and things to remember to consider, but the key is not the specific accuracy of any specific climate maps unless you are specifically making maps of hypothetical worlds guaranteeing climate accuracy in their Koppen zoning.
The goal should probably be to produce quality content in the setting While your setting may not be totally accurate, it would behoove you to make sure it is not so inaccurate as to be glaringly obvious while also not specific enough to be easily dated in 5 years. Depending on what the prose is for of course...