You'd be hard pressed to find cactus around here in Owyhee. It exists, but not so's you'd find enough to stick your nose in it.
Except for Bodie. He found it, and stuck it where it hurts - his nose, which he uses for just about everything - eating, sniffing, feeling.
Even if the horse held still, you obviously don't want to try pulling it out with your bare hands, because the other spines will stick in your skin. You don't want to try pulling it out with gloves, because even if you get a grip on it, you'll probably poke it further in, or poke other spines in his nose.
Best is to use a comb, and rake it over the area quickly, flipping the whole cactus piece out. Fortunately I haven't found any single cactus spines in any of the horses. These can be a nightmare to remove, often requiring veterinary sedation and subsequent treatment, as many people living in Arizona have probably learned.
Bodie hardly knew what happened, and right after I swept the cactus off his nose, I gave him a good (much appreciated) scratch.