Oh dear, don't get me started on the warmblood debate.
Ok, YES, originally, warmbloods WERE derived from hot bloods crossed with cold bloods. HOWEVER, they have now been bred into specific breed registries - i.e. hanoverians and holsteins. Warmbloods are now as specific a breed as say the hot bloods - thoroughbreds, arabs.
But you would be very misled to believe that a cold blood x hot blood could be registered as a warmblood. A WB sport horse maybe, but not a genuine warmblood registry such as the hanoverian stud book.
If any old cold blood x hot blood could be registered as a hano or similar, the Europeans must be wasting their time with such stringent breeding regulations, and I must also have wasted a hell of a lot of money on buying my hano yearling.