I don't see that everything except Canada, Alaska, Greenland, Siberia and Antarctica was inhabitable. For instance in Eocene the climate remained fairly warm and homogeneous (the most uniform in the Cenozoic).

From the equator to the poles, forests grew. Fossilized remains of cypress and sequoia have been found on the Arctic Ellesmere Island, and palms — in Alaska and northern Europe.

Equatorial and tropical forests (with palms, fig trees, and sandalwood trees) persisted in Africa, South America, India, and Australia.

Eucalypts, sequoias spread widely, and new types of broad‑leaved trees appeared.

By the end of the Eocene, rainforests were preserved only in the equatorial parts of South America, Africa, India, and Australia — due to the onset of cooling.