| MadSci Network: Earth Sciences |
The earth's magnetic field ("magnetosphere")is formed by electrical currents in the molten iron at the center of the Earth. It stretches out into space all around the Earth, and is pushed around and stretched by the "solar wind", a stream of very thin hot gas which blows outward from the Sun. As the solar wind changes, so does the magnetic field. Magnetic field changes are also caused by changes in the flow of the molten iron in the Earth's core. In fact, the Earth's magnetic field actually reverses direction once every several hundred thousand years, and for a short time during this process the magnetic field is nearly gone.
Most scientists think that changes in the magnetic field have very little effect on the Earth's weather and climate. The reason is simple: magnetic fields only act on moving electrical charge. Electricity flowing through a wire is an example of moving electrical charge. But with the exception of lightning and other very powerful electrical discharges, the lower part of Earth's atmosphere does not allow electrical charge to move through it, so it is unchanged by magnetic fields.
Lightning is too powerful and too quick to be affected by Earth's magnetic field -- I have previous Mad Scientist's Network answer which discusses this.
The very upper part of the Earth's atmosphere, the ionosphere, does allow charged particles to move around, and so would be affected by changes in magnetic field. But those changes are probably not what you'd call "weather": I don't think they will affect temperature, wind, pressure, cloudiness, or rain or snow at ground level.
According to an article in the Christian Science Monitor,
"no correlation has been established between reductions in the magnetosphere and mass extinctions as a result of exposure to the solar wind... Nor have any climate variations like the onset of ice ages been conclusively connected to changes in the magnetic field."This is a well-written article from a reputable magazine, but I should warn you that the web site where I found a copy of it is full of people who're convinced the world is about to end.
So, no obvious changes in Earth's climate have occurred during past magnetic reversals. This is confirmed by NASA's "Ask a Space Scientist" site.
You'll have some trouble finding articles which discuss this effect (I know I did): the reason is that scientists aren't very interested in studying things that don't exist -- or which we have good reasons to doubt.
Many of the sources (particularly websites) which you find which claim to find a connection between magnetic fields and weather are "crackpot science", which uses bad logic and carefully chosen (or even invented!) data to support the conclusion. You shouldn't just take my word on this: you're entitled to come to your own conclusions, but I want to warn you of the danger.
A fairly complex description of changes of the Earth's magnetic field is given by this paper.
Try the links in the MadSci Library for more information on Earth Sciences.