Jotunn are very rarely specified as "ice giants" in Norse Mythology and are actually described as being very diverse in appearance and abilities. Laufey was never specified as an ice giant (in fact she is sometimes referred to as an Aesir) and in some texts it says she was impregnated with Loki when the jotunn Farbauti struck her with lighting. 

He not always said to be a fire giant in mythology, but it appears from time to time and I enjoy the idea