I agree with the answers given, for the most part. At 8, the child is probably not under-dressing to make a fashion statement. The worst thing that might happen is someone is left lugging around an extra layer (isn't that partly what parents are for? ;)) and everyone learns. Eventually stop lugging around the layers.
It's important to respect a child's decisions. If she was mistaken and wants her coat back, and you point it out to her, you should consider applying the same principle to yourself and admit when she was right. That's one way of showing respect. (If you don't point out her mistakes, you can give yourself the same slack for minor things.)
Finally, the worst thing that might happen is not a cold or pneumonia. People might be uncomfortable when chilled, but it doesn't make them ill. This is an 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."
If this is why your wife wants more layers, not less, you can tell her the following:
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 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.
'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