The height of a horse on Horse Reality is displayed in the information box on its profile. The final height of a horse depends on its breed and its genetics.
Each horse breed has an accepted height range. You can find the minimum and maximum height of each horse breed on the registries page.
As time passes and a newborn foal grows older, it also grows taller. Horse Reality horses grow each month and only stop once they reach 7 years of age.
The inheritance of height works differently from any other genetic stats in Horse Reality: each horse only has one height allele, not two. A foal inherits the height allele of its dam or sire + RNG within the limits of its breed registry. It's not possible to breed a horse with a final height outside these boundaries.