1. Northern lights are caused by the solar wind hitting the Earth's magnetic field.
2. They have no relation to greenhouse gasses.
3. Most common color is green.
4. Most rare color is blue.
The Northern (and Southern) lights, more scientifically called aurora borealis (and aurora australis in the southern hemisphere) result from several things interacting with each other.
You may have seen pictures of the Earth's magnetic field, looking very much like the classic picture made when sprinkling iron filings on top of a piece of paper over a bar magnet. Lines of magnetism connect the North and South poles in ever expanding loops.
Charged particles have great difficulty crossing these lines, though its easy for them to travel along them. As a result, if charged particles get injected into Earth's magnetic field, they more or less move along the lines -- and the only place the lines approach the Earth's surface is near the north and south poles -- more specifically, the Earth's *magnetic* poles, and not the poles of the Earth's rotational axis.
When a charged particle hits the Earth's atmosphere, it can excite atoms to higher states of energy -- these atoms can then decay by emitting light. This light is what we see as an auroral display.
Now to address your questions: First, how do charged particles get into the Earth's magnetic field? The Sun is constantly throwing off charged particles in the form of a fast stream of material which we call the Solar Wind. When this "wind" blows past the Earth, it presses against the Earth's magnetic field and even bends it back, like a tree bending in the wind. In general the magnetic field keeps charged particles from the solar wind from getting in, but some do leak across. This explains the aurora which happens more or less constantly from dark skies at very high latitudes. Sometimes the solar wind has a stronger magnetic field of its own threading through it, and if this magnetic field happens to be opposite in direction to the Earth's, then a sort of "cancellation" can take place, allowing a transfer of large amounts of charged particles into the Earth's magnetic field. This is what causes auroral storms, when the aurora can be seen from more central latitudes, and when it can become much brighter at extreme latitudes.
These charged particles entering the atmosphere can interact with all of the gasses present in our atmosphere, but the gas which produces most of the visible light which our eyes see is oxygen. High in the atmosphere, it is present not as a molecule, but as individual atoms. It tends to emit two colors -- red, which it does best when excited at very low pressures, which take place very high up, and green. This is why most auroral displays are green, shading to a faint red at their upper reaches.
Intense displays with rapidly moving particles can reach down into the lower atmosphere and excite nitrogen and oxygen molecules: this causes bright green aurora with bright red lower edges.
At very central latitudes, like the southernly United States, aurora are very rare and can only be seen during great auroral storms. The particles that can hit the atmosphere here are only very slowly moving ones which have lost most of their energy weaving their way through the Earth's magnetic field to get to these central magnetic lines: they can't penetrate deeply into the atmosphere and only produce the red glow of oxygen atoms being hit very high in the atmosphere.
Greenhouse gasses such as carbon dioxide and methane are present in the atmosphere in only tiny amounts, and play no significant role in visible aurorae.
Though aurorae are seen best from cold climates, it isn't the cold that produces them. It just happens to be cold at high latitudes.
As far as other colors, sometimes blue-violet aurorae can be seen faintly. This can only occur in rare circumstances when the region of particle interaction with the atmosphere is still being illuminated by sunlight while it is already dark on the ground. When both sunlight *and* charged particles excite gasses in the atmosphere, especially molecular nitrogen, it produces a bluish-purple color. Very few people have ever seen this color of aurora.