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1.
A Male with a big dick, who walks around like he has a big dick, or has been told he has a big dick.
although, the term can be used to describe Males or Females as it is describing a personality or attitude as being extremely self-assured or narcissistic.

When used to describe Females, "Horse Swag" means cocky, bitchy or having a "I Know I'm the Shit" attitude.

Horse Swag can also define the demeanor of someone who does heroin, as "Horse" means heroin
Girl #1: "OMG Michael is hung like a horse"

Girl #2: "Figures, he walks around with so much Horse Swag"
by D1andOnly January 06, 2013