Catching a cold outside in winter?
This is a pretty old old-wives tale, taking many forms: don't go out into the cold while it's raining, or without a hat, with wet hair, without a warm coat or scarf, without boots, etc., "or you'll catch your death of cold."

The old wive's tale was immortalized by Jane Austin in her book, Pride and Prejudice, when the heroine's sister Jane falls ill after getting a soaking in the rain.

This has been studied extensively. A New York Times article describes one such uncomfortable-sounding study:


  In the 1950's, Chicago researchers repeated the experiment on a larger scale with several hundred volunteers sitting in their socks and underwear in a 60-degree room before being inoculated with infectious mucus. Others, in coats, hats and gloves, spent two hours in a large freezer. The conclusion: all 253 chilled volunteers caught cold at exactly the same rate as 175 members of a warm control group. 


In other words, being cold had no effect on catching a cold.


  A survey of the medical literature shows that for more than a century, scientists have invested an extraordinary amount of time and energy in debunking this old saw, with the aid of a small army of shivering, sneezing volunteers. But despite their efforts, the link between colds and the weather still lingers and continues to inspire yet more research.


A 1968 experiment studied the effect of (among other methods of chilling) a cold water bath at several stages during and after inoculation with rhinovirus (one of the many viruses responsible for the common cold). No effect.

Yet the studies continue, because anything shown to decrease the incidence of the common cold would be beneficial to the sufferers, as in the US alone, 75 to 100 million physician visits are due to the common cold, and millions of days are lost from school and work.

But what has never been proven is that getting chilled in any way causes one to come down with a cold.

There are a lot of studies that fail to show a corellation. However...
there are a handful of small studies that show that having cold and dry nasal mucosae increases the susceptibility of infection when inoculated with rhinovirus, though. So, if these studies are accurate, then being in the cold when exposed does increase the chance of becoming symptomatic.

'You'll Catch Your Death!' An Old Wives' Tale? Well...
Exposure to Cold Environment and Rhinovirus Common Cold — Failure to Demonstrate Effect
Acute cooling of the body surface and the common cold