In Jungian psychology, the animus can be identified as the totality of the unconscious masculine psychological qualities that a female possesses. It is an archetype of the collective unconscious and not an aggregate of father, brothers, uncles, or teachers, though these aspects of the personal unconscious can influence for good or ill the person. Jung postulated that women have a host of animus images.[a]
Adam and the Cowboy taken together, comprise a kind of 'split animus' within Diane. Adam is the more 'intellectual' of the pair of men, and the fact that he wears black clothing throughout the movie symbolizes that Diane's intellect, has been 'cross-contaminated' with contents from her psychological shadow. In Jungian psychology, the shadow is an unconscious complex defined as the repressed, suppressed or disowned qualities of the conscious self.[b] Recall that in Diane's dream, Adam beat up the Castigliane brothers' limousine with a golf club; this indicates that Diane's shadow consists, in part, of an instinct tending toward violence. One reason we don't see Diane herself actually commit any violence during the movie, is because she represses or suppresses this instinct.
The Cowboy represents the more conventionally masculine of the two images of Diane's animus, and he also represents that part of Diane's animus that serves as mediator between her unconscious and conscious mind, and that can act a a guide. When the Cowboy speaks to Adam in Diane's dream, he is, in reality, speaking to Diane while she's in her dreaming state, and he is attempting to get Diane's intellect to listen to her unconscious.
a. Wikipedia, 'Anima and animus'. Web, n.d. URL = https://en.wikipedia.org/wiki/Anima_and_animus.
b. Wikipedia, 'Analytical psychology'. Web, n.d. URL = https://en.wikipedia.org/wiki/Analytical_psychology.