Here's some work I've been doing at Wikipedia:
Exposure to cold conditions, or the moving between cold and warm environments, is not a cause of the Common cold or Influenza. Moreover, the development of colds and 'flu are not encouraged by such exposure. Cold weather often forces humans to congregate indoors, which encourages the spreading of airborne viruses. (Long term exposure to cold conditions can, however, lead to Hypothermia, which is a much more serious problem)
Infection with a cold virus affects thermogenesis. This makes people associate post-infection shivering with situations in which they were exposed to cold that intensifies shivering (e.g. wet hair, draft, long wait on a bus stop, etc.). This association helps propagate the myth.
A cold virus often irritates nasal passages and encourages sneezing. Sneezing can also be caused by other conditions, notably exposure to colder air temperatures. Cold weather can thus cause sneezing, but sneezing is not necessarily an indication that a person has "caught a cold".
If cold weather were directly linked to the spread of the common cold, then it could possibly be demonstrated by comparing the infection rates of people who live in colder climates (such as Iceland or Greenland) with people who live in warmer climates (such as countries close to the equator). Studies done in the 1960s found no significant increase in infection rates in people who live in colder climates.
One reason why so many people link exposure to cold weather to "catching a cold" is via a logical fallacy which assumes that Correlation implies causation. Colds are certainly more prevalent during colder periods of the year, but it is wrong to assume that the two are directly linked.
The "Correlation implies causation" fallacy can also apply to popular treatments for colds and flu symptoms, whereby a sufferer associates their improving health to certain cold remedies, when in fact their improving health would have occurred with or without these remedies. Popular remedies can also have a "Placebo effect", whereby a person who believes in a certain treatment "feels" better as a result. Some of these popular treatment are:
Echinacea. Scientific studies into the effects of Echinacea have shown no measurable positive effect on those suffering from colds or 'flu.
Vitamin C. Vitamin C can reduce the incidence of colds amongst physically stressed people by up to 50%. Amongst ordinary people, a 200mg daily dose had no effect whatsoever in reducing the incidence of colds.
Zinc lozenges. A 1999 study showed that the effects of zinc lozenges for treating the common cold are inconclusive.