The safety sense leaflet says that severe icing is most likely to occure between 0 and -10 deg. However, in my ATPL notes somewhere, it states that severe icing conditions should be assumed between +3 and -10. Below -20 there is virtually nil/very light icing.
The freezing rain that bookworm alludes to is the ATPL examiners favourite hazard of flying in the sub-zero cold air below a warm front. To escape such a predicament, the tested resolution is to climb.
The only icing not related to cloud or precipitation is hoar frost that forms when descending quickly through an inversion.