You could get away with calling her an American Warmblood or a Lippizaner Sporthorse. ..................... Canadian Warmbloods are pretty much famous for being PMU babies of uncertain ancestory.
No....not even an American Warmblood.
IF and only IF the horse is registered and APPROVED AWS or AWR can it be called an American Warmblood.
Canadian warmbloods are simular in that you can have what is truly considered warmblood but in the auxilliary division you can have anything including gaited horses. Draft crosses are discouraged but do exist.
The OPers horse is a TB cross or a Lipp cross. Get it registered something and only then can it be called anything different.