This was heard in a phone conference. The context indicated that the speaker was thinking of straw man. It is a nice conflation of “straw man” (a form of argument and an informal fallacy based on giving the impression of refuting an opponent’s argument, while actually refuting an argument that was not presented by that opponent) and I think “horse of a different color” (something completely different, particularly in comparison of something else). Both expressions refer to comparisons or substitutions. “Trojan horse” (something that seems good or useful but is really something to cause harm in the future) may also be in play, as again it refers to a substitution or comparison. The speaker probably linked “straw” with “horses” instead of “men” which would be logical, as horses sleep on straw.
Speaking of straw man arguments, they are incredibly abundant in today’s political theater as fallacies seem to be successful tactics. For example, Trump wants a wall on our southern border. That leads Republicans to support the unfair assumption that anyone who opposes the wall is for open borders; Trump even went so far as to accuse House Speaker Nancy Pelosi of supporting human trafficking because she opposes the border wall. However, immigration is not an either/or proposition. Both sides are in favor of border security, but if the Democrats must defend themselves against the false charge that they want no restrictions at all on immigration, they waste time and energy that could be spent on reaching common ground. Thus the straw man that Democrats are distracted by and find themselves attacking instead of the real issue.
A big thanks to Forrest Morgan for hearing this one and passing it on!