Well yes, if it's cold enough to freeze their nuts off...Seriously, cold doesn't do too much damage. As 'Spaw points out, heat is a worse problem, both extreme humidity and extreme dry heat. Of the two the latter is more serious. Also rapid changes from very cold to warm can be a problem. If seen this once or twice from instruments coming in from -20oC into a hot and sweaty pub or club and MIdchuck's comments above are right to the point.
mcmoo