There are these warm blood carriage horses that have become quite rare (the Cleveland Bay is one such horse). They were bred to provide a nice consistent type and color so carriage horses would be matched.
I am unfamiliar with this Latvian breed.
What has happened is that a lot of these horses.. bred for carriage work.. are not being bred anymore and the breeds are becoming rare.. or even extinct (some light draft horses as well such as the Suffolk Punch). The warmbloods that are being bred are largely being bred for sport horses and come from the ranks of former cavalry mounts. Meanwhile, the warm bloods who used to bring the guns up in massive hitches are being passed over.
I think this is a shame. These carriage warm bloods are often quite good horses with very stable dispositions.
I do not know if the Latvian breed is rare but looking at this horse I see a field hunter. His shoulder is a bit steep and he is over weight.. but look at the nice bone, decent hind leg and so forth. Hooves might be a bit long.. but what a nice solid horse all the way around.
I think the breeders of warm bloods for sport horses are missing the ball in not looking at these carriage horse breeds.