I would like to say the badminton racket temperature in cold weather is probably a myth.
I have had my Yonex MP-21 and VT-70 (before I sold it) in my trunk overnight (1 or 2 nights) under Canadian winter no problems.
The string tension is around 22-23lbs..
I do not know the effects of leaving my racket in the car for more than 2 overnight though..
The racket are fine when used in play, and have no signs of cracking, or paint chipping off easier.. (*Imaging the Carbon graphite used in planes and space shuttles, it would have to endure -50 degC or lower)
Though I DO HAVE TO SAY is the the string feels dull and dead after leaving it in my car outside in Canadian winter overnight. The string on the racket just do not feel as good as before, it feels dead...
Also if I leave my plastic (Mavis 350) or feather (Aeroplane Bk Label) overnight in the cold, the cork feels dull as well, and the feather flakes off fast (probably due to dry humidity in Canada)...
I don't think that cold will effect rackets that much if the racket has some time to warm up before being played. Also, keep in mind that your string tension is relatively low. I'm not sure that you would have had the same experience with a 28lbs string tension.
One thing that is for sure though is that if you leave your racket in the cold with a decent tension in the strings (say 22lbs+) and you play with it right away, the strings will break pretty much instantly.