The Himalayans were only one cause of transitioning to an icehouse world. Others (and more important) are plate tectonics thermally isolating the polar regions from warm marine currents which lowered the temperature threshold for extensive glaciation at each pole with each pole having very different glaciation characteristics because of their landmass distribution and resulting ocean circulations and orbital forcing which triggers glacial periods when temperature is close to the thresholds. You can see this on the oxygen isotope curve.
But none of this has anything to do with comparing the last to interglacial periods of which disproves CO2 driving the planet's temperature.