CD players not working right in very cold temperatures is normal. Mine actually has a "Low Temp" indicator on the display that comes on when it's below ~20 degrees. Where I live we get nighttime lows in the negatives this time of year.
My Pioneer 590 will sometimes not respond the first time you push a button after you start the car. But it gets in the negatives here all the time, so I'd say it does pretty good.