Eventually the continents became separated, and when the glaciers advanced, they pushed the remnants of the plant life (including seeds) South. In the Americas and Asia, the mountain ranges run pretty much North/South, so the plant life got pushed along the valleys to the southern edge of the glacier fields, where they seeded themselves and grew until the glaciers retreated. Then the plants gradually migrated North again as the glaciers retreated and exposed the ground.

In Europe, the mountains run in a pretty much solid East/West line. So the glaciers pushed the plant life up to the top of the mountains, where it couldn’t survive, and many of the plant species died out. That’s why we have American and Asian versions of plants (like rhododendrons and magnolias), but there are not any equivalent European species.