Technically, to the truest definition of the word, a coldblood and a hotbloodhorse bred together gives a warmblood. So by definition, a warmblood can never be considered a purebred, despite the fact that people will always say "oh, he's a purebred Holsteiner/DutchWarmblood/Trakehner" The only true purebred horse is likely the Arabian.
However, warmbloods have evolved into very distinct and seperate breed from the old coldblood/hotblood cross, especially in Europe, as breeding is MUCH more controlled there than it is in the States/Canada. So you could say that a true warmblood - how the world thinks of warmbloods - is a horse that has a pedigree that can be traced back at least 4-5 generations that is composed of sport horse bloodlines.
Your horse would be called a draft cross :) or A lippizaner cross