Excerpted from an electronic copy of the manual (which appears to be hosted on a retro Amiga gaming website, but the manual text was identical across versions except for perhaps the Mac version, if I recall correctly):
Even though you don't see the seasons change or the rains fall, and
you don't feel the wind blow (other than an occasional tornado or
hurricane), there is a climate model in SimCity 2000 that affects
your city. Weather reports are available in the newspapers.
Weather trends are generated on a monthly basis, when the
simulation looks at the current trend and the season and throws in
a certain weighted random element and decides the next trend. The
different trends are: cold, clear, hot, foggy, chilly, overcast,
snowy, rainy, windy, blizzard, hurricane and tornado. Blizzard,
hurricane and tornado are the least likely to occur.
Each trend has a temperature, a wind and a humidity element. In
general, temperature affects the water supply, the availability of
solar power, and the likelihood of fires and riots; wind affects
the availability of wind power, and humidity affects the water
supply. These effects combine in various ways in the various
trends.
I don't remember ever really noticing any of the more subtle effects described above, but I was pretty young when I played SC2k regularly.