comment on the different biomes:
Green: If I understand correctly, there are two different green ? One for savanna and the other for the tropical rainforest?
Pink: East coast barely have any maritime climates. They tend to have continental climates because the dominant winds come from the interior of the continent and so have a higher temperature gradient. Meaning that the east coast should have more pink and almost no purple.
Purple: A cool temperate climate would either be a cool continental climate (Canada, Scandinavia) or a cool maritime climate like Iceland, Norway and parts of Southern Chile. The latter is not very common.
Using the Koppen climate classification https://en.wikipedia.org/wiki/K%C3%B...classification
The former would probably fall under Dfc, Dsc or Dwc. It's the boreal forest dominated by pinetrees.
Personally, I would use purple as continental cool and pink as continental temperate.
I would also add a darker purple for the subtropical climate (Sun belt, Central China, southern Brazil)
And another one for the tundra. Some small parts at the tip could be cold enough and the places at higher altitude as well.
And possibly another one for the glaciers if it's necessary.
Now, some more specific comments:
In general, the map is pretty good.
In my opinion, the blue area goes too close to the pole. Above a certain latitude (maybe 60) it tends to stick only to the coast if the oceanic current are warm enough. Also, mountains do block the influence from the sea making temperature in the east more contrasted.
The tropical forest sticks close to the equator and is pretty narrow, like in Africa. This is because at least half of the winds blowing are dry (they blow north from the dry continent). The same reason why Arabia is dry is because the winds blowing over the peninsula mostly carry dry air from Asia and parts of Africa.
While it's true that the islands are blocking the surface currents, but since they are pretty much at the equator, the impact is limited. I expect that the north ocean will be colder but not that much.
It could have a major impact on the general water circulation on the planet but we don't understand well enough the impact of deep oceanic circulation on Earth to begin with, so we can only speculate.
I've made my own version of the map using your colour scheme but adding some colors as I mentioned above.
There are areas with only small changes where both versions could be good, it's hard to tell.
kottek_et_al_2006 copie.jpg
You can see the original Koppen map for 2006 is located here (the gif link) : http://koeppen-geiger.vu-wien.ac.at/present.htm
And if you scroll down a bit, they made a revised version for 2017. If you look carefully, you can notice some changes between the 2 maps .
This brings me to my last point. The climate has changed over the course of the 20th century and continues to change. With that in mind, having an Earth-like climate becomes somewhat less clear and there is some margin of error.