I know a lovely Fjord x anglo arab
and yes to say that the fjord horse registry frowns on cross breds would be putting it lightly.
The Fjord Horse National Stud Book Association of Great Britain which is authorised to issue passports run 3 registers; Register 1 for Pure Breds with proven lineage, DNA, microchipped Register 2 True to Type and Register 3 Part Breds. The top stallions are often only available to Register 1 mares http://www.fjord-horse.co.uk/index.htm
The strict rules for Register 1 is very important as the gene of the fjord is so pure it is dominant (as in previous posts) and crosses often appear fjord but the nature may not be!
I would add I have found ours extremely quick to learn