The aims of this observational study were to (1) define which animal’s phenotypic characteristics determine social position in the context of a commercial organic farm with mixed herd (horned and non-horned cows) and (2) determine the influence of social position on the time at the feeder. We took the following measurements from 27 dairy cows in lactation: body mass, age, body condition score, body length, withers height, distance between horns, horn circumference and length. Replacement and time at the feeder were recorded for 1 h at the time of supplementation. Dominance values for each animal were calculated and the herd was divided into three social categories: dominant (D), intermediate (I) and subordinate (S). Age, body length and body mass influenced (p < 0.001) dominance value of all animals. The presence of horn influenced (p = 0.034) the dominance value of the I and S animals because it was a unique characteristic of these categories. Dominant (84.3%) and intermediate (75.2%) animals spend more time (p < 0.05) at the feeder than the subordinate (59.5%); however, dominant animals tended (p = 0.093) to spend more time at the feeder than the intermediate animals. The social position of an animal was influenced by its age, body mass and body length, and its social position influenced the time at the feeder.