The warning like we had on a Volvo was discrete enough, but the driver easily misses that.
At my place we drive a lot at temperatures around zero Celsius and I can assure you that a temperature warning beep would quickly become very annoying.
It also does not always become slippery when ambient temperature reaches zero, if the car gives a warning at some fixed temperature, the car may be driven another 50 miles before the road actually becomes slippery and the warning tone has been forgotten. It is the driver really who would have learn to identify when the roads become slippery, the car would never be able to estimate it accurately enough and if it cannot do it properly, then better not to do it at all (some simple drivers would learn to count on the car giving the warning).