This idea has been around a while but gained new oomph with the 2003 publication of the science-history book Napoleon's Buttons, by Penny Le Couteur and Jay Burreson. The story says the army Napoleon led into Russia in June 1812 had been outfitted, possibly as a cost-cutting measure, with uniforms held closed by tin buttons. When temperatures dropped during the French retreat later that year, the buttons crumbled, leaving troops exposed to the murderous elements.
Why would this happen? Well, stuff that's made mostly of tin is susceptible when subjected to cold to what's known as tin disease or tin pest, which causes regular metallic tin (also called white tin) to become gray, powdery, and brittle; when gray tin comes into contact with previously uncontaminated white tin, the condition can spread like a fungus. This change in the bonding structure of tin atoms starts very slowly at 13.2 degrees Celsius (56 degrees Fahrenheit) and speeds up as the temperature decreases, reaching a peak between -30 and -40°C.
So tin disease is real, but is the buttons story true? (Don't ask Le Couteur and Burreson, who are pretty terse and noncommittal on the topic considering it's the name of their book and all.) Me, I'd say probably not. Consider: (1) Tests performed with tin ingots suggest it'd take maybe 18 months at lowered temperatures to result in appreciable flaking. Napoleon's Russian campaign lasted less than half that long and didn't encounter severe cold until the very end. (2) It's not like tin disease was a big secret in 1812; it had been observed for centuries. Tin alloys like pewter were commonly used for buttons, and alloying tin with just 5 percent lead is enough to keep the problem at bay. (3) A mass grave of Napoleon's soldiers was discovered in Vilnius, Lithuania, in 2002. Helping to identify the 2,000-odd bodies as casualties of the hellish 1812 retreat were numerous regimental buttons, many made of tin alloy and still legible after 190 years in the ground.
You also sometimes see tin disease blamed for the failure of Robert Scott's South Pole expedition in 1912; the idea here is that tin solder used on kerosene cans deteriorated, allowing precious heating fuel to leak away. Again, not impossible, but unproven.