I never leave home without a small first aid kit (including some survival gear, like a way to make fire and purify water), my knife (or a leatherman tool), and a rain coat. Out here it’s easy to die from exposure, so best to be prepared.
Can I add one thing to others’ lists that has saved me in a pinch many times? A 100% silk wild rag! Use it like rope to tie up a broken cinch buckle, use it as a collar to catch a loose horse, use it as a sling or to bind a wound on animal or human, use it as it’s intended to keep your neck warm (especially appreciated if a storm comes up or you get left out at night with an injury), use it to blindfold an injured or frightened horse, use it as a basket to carry wild berries or mushrooms, or even use it as a silt filter before purifying your water. Silk is super lightweight, warmer than wool and much softer against your skin. Get it in a neon color specifically to keep in your saddlebag, and it also functions as a signal flag for a helicopter landing or search and rescue. I wear one about 350 days a year, so I always have one with me, but I keep a second one in my saddle bag just in case I should need it, and the many uses never cease to amaze!
Also, regarding the handgun or pistol: I often carry one on long rides, but I want to specify that’s to protect myself from other humans (trespassing hunters are also armed, so I had better be as well!), or to put down an injured animal. Pistols are NOT especially effective against wild animals! Did anyone see that great study last year that showed that 50% of the time in a bear attack, a person with a gun still ended up injured (sometimes from the bear, sometimes from their buddy shooting them in an attempt to shoot the bear). In contrast, in a bear attack where bear spray was used, only 2% of the time did someone still end up injured. FIFTY percent versus TWO percent??? No contest: carry bear spray every time. It’s just as effective against wolves, mountain lions, humans, and the neighbor’s attacking dog as it is against bears. Okay, off the soapbox. Cool study, though. Changed my mind about how frequently I grab the spray.
Oh! One more thing! For those leave-no-tracers who pack in the backcountry, bring a teabag in a ziploc for your used toilet paper/sanitary products. The tea bag will absorb wetness and odors, makes it way less gross. 
