The studbook of Pura Raza Menorquina horses only permits the use of black-coated animals with a small quantity of white marks as breeding stock. Its breeding program uses linear morpho-functional traits as selection criteria. Our aim was to estimate the genetic parameters of linear morpho-functional traits, and reveal relationship of quality of black coat color (QB) and percentage of white marks (WM) with the other morphological and functional linear traits in this breed. A total of 46 linear traits were scored by four appraisers using seven classes, with a total of 772 records from 333 animals (≥4 years old). Univariate animal models using a Bayesian approach were used, with a pedigree of 757 animals. Sex (two) and appraiser-season (13) were included as fixed effects, age as a linear covariate, and permanent environmental and additive genetic as random effect. The heritabilities of the morpho-functional traits were low to medium (0.09–0.58) and matched the range in the bibliography. Heritabilities for coat color traits were 0.36 for QB and 0.23 for WM. The highest genetic correlations were obtained between QB and upper neck line (0.816) and between WM and form of the hoof (0.638). The negative signs of most of the genetic correlations between WM and the functional traits is also remarkable, contributing to the selection of functional traits against the presence of white marks in this population. A clear genetic differentiation was observed between animals with better breeding values for QB and WM, corroborated by a study on founders. In conclusion, QB and WM could show different genetic backgrounds.