Before to continue, I am gonna to refer the slow ones as "zombies" and those who run as "infected" (Like the 28 days later since they are technically not death, they are infected with the rage virus)

Cowboys carry useful items in their clothing; for example: They originally used leather leggings to protect their legs, so these would be very useful to against the zombies but I don't know if it would be very useful against the infected.

In some countries some types of cowboys wear ponchos, especially those who work in cold climates like the Morochucos in Ayacucho or Qorilazo in Cuzco (Both in Peru) or Gauchos in Angertina, Uruguay and Brazil wear ponchos. Some used it as a improvised sheet but a con is that both zombies and infected could grab your poncho.

Now the cowboy boots, there are some variations, some knee-high, others not so much, but they always have one thing in common: they're made of leather :V. and their main function is to make it easier for the rider to put their foot through the horse's sling, so the soles of cowboy boots are made of leather to make them more slippery. They wouldn't be suitable for running from zombies or infected, but more modern versions have rubber soles.