As a result, the planet is cooling and has accumulated a blanket of ice.

You think the planet is cooling because it's winter or what?

It's such a light element it probably all boiled away while your planet was cooling.

The planet was cooling, and its core presumably no longer functioned as a dynamo.

If these could be exposed to the atmosphere then the planet would cool and its atmospheric pressure decline somewhat.

Over time, the planet cooled and formed a solid crust, allowing liquid water to exist on the surface.

The planets may not have cooled as yet.

Once the winter storms arrived, the planet cooled rapidly.

Over the past 50 million years, the planet has been gradually cooling as those greenhouse gases dwindled.