But instead imagine an ice covered world - along the lines of the planet Hoth of Star Wars fame. This has happened in the Earth's past and it was far more severe than you could imagine. The recent "Ice Ages" are a pale imitation of these frozen times as there was still warm tropical regions (though compressed) on the planet.
Back in the distant past over 2.3 billion years ago, the entire planet was frozen in a phase appropriately known as Snowball Earth. Most if not all the planet was encased in a shell of snow and ice up to a kilometer thick. Yet life survived - even flourished deep in the oceans for tens of millions of years until conditions changed and the Earth "thawed out".
It has been theorized that this first "Snowball Earth" (there have been others - the last between 750 to 580 myr BP) was in part the result of biogenic changes in the atmosphere - from a methane (a strong greenhouse gas) and CO2 rich one, to a version dominated by nitrogen and oxygen. Other possible causes include changes in the axial tilt (which causes our seasons) and positions of the continents due to plate tectonics. An excellent review of the Snowball Earth Hypothesis can be found by making with the clicky.
What defines a "natural satellite"? Does it have to have an elliptical orbit or one that is even stable for that matter? In reality, there are a number of co-orbiting asteroids that "share" the same orbit with our planet. These objects have nearly the same orbit, though they might be slighty slower or faster than the Earth. Sooner or later, they will encounter the much more massive Earth and then begin a weird orbital dance as the asteroid corkscrews around our planet.
One of the most recent co-orbitals, a 20 meter wide rock known as 2003 YN107 is about to depart our planet after 7 years of orbital dance. An even better known co-orbital is 3753 Cruithne, that has a neat-looking "horseshoe" orbit about the Earth.. Unlike the other asteroid, this one has a metastable orbit - which is a *good* thing since it is 'dino-killer sized" or about 5 kilometers across.
Co-orbitals not only stay near our planet for long periods of time, but could make a asteroid mining a distinct possibility in the not so distant future.
Now imagine this..
An interesting use of this idea would be co-orbiting, habital planets. Imagine two planets in nearly the same orbit, and every 50 to 100 years they would make a close pass and "switch places". Perhaps in periods of a 1000 years, they past would pass so close (let's say 20,000 to 30,000 miles) that you would have massive earthquakes, tidal waves and wholesale destruction on a planetary scale. Planetary orbits could be shifted dramatically and it would take many hundreds if not a thousand years before the normal orbital cycling were to resume again.
Now place two colonies on these planets and 'stir'...