I started to respond to this post by Haiku Farms in comments but decided it would be better to make it into a whole post. I agree with her self-defense post up to a point. A person who decides to get a gun and never shoots, just gained an expensive & odd looking paperweight; so she's right - if you don't intend to practice, there's no point in getting a gun. However, I don't agree that you have to be a hunter or a soldier to shoot well; heck, you don't even need constant access to a range. You can practice grip, target acquisition, posture, etc with snap caps while watching TV. A gun is a tool, you don't have to make a hobby out of it, just learn to use it.
The entire premise of the post is having to defending yourself, not making an escape, not barricading until help arrives (these options were covered in previous posts) so why not have & learn to use the best defense weapon out there? I, at 5'6" and 145lbs, am not going to pit my strength against a goblin intent on doing harm - no matter what size skillet I may have access to. Intent is everything in these scenarios; the goblin has already planned on causing harm. You have to decide what your own intentions are when someone threatens you (and I agree with Newbius's post on what a life is worth). Defending yourself is the final option, you've decided that you cannot escape and your life is in danger.
In regards to being able to hit a target at close range (< 25yrds), I have up to 16 tries to neutralize the threat - I doubt I'd have that many tries to stab them with a pitchfork or beat them with a frying pan before being overpowered. I also don't see someone advancing into gun fire, even if I am missing. I can see a goblin risking a whack or two with a pan to subdue his victim. A gun is the greatest equalizer and if I've made the decision to fight, I want as many factors in my favor as possible. Shooting, of course, would be the last resort in any goblin scenario; if I can avoid, flee or diffuse a dangerous situation I will. However, if I'm afraid enough to draw a gun I'm shooting to kill, not to wound and certainly not to frighten.
Of course, adding a 1000 lb creature into the mix makes things more difficult. As mentioned in Haiku Farm's post, unless you've desensitized your horse to gunfire you're asking to be dumped firing from its back. That said, if I'm contemplating shooting while mounted, things have gone so far beyond pear shaped that being dumped is the least of my concerns. The only (human) situation I'm not running away from is a goblin with a deadly weapon; anything else, run-pony-run. If someone's threatening me I'm shooting mounted and taking the associated risks.
I do advocate desensitizing your horse to gunfire regardless of your choice of self-defense. How will you know if someone else on trail isn't armed or someone isn't hunting nearby or that a goblin won't light off a few rounds just so you're thrown. You desensitize them to a host of other sights and sounds, why not one that could save your life? I'd recommend Cowboy action shooting as a place to start for information. It's a large and healthy organization and they're one of the friendlier groups of horse people I've ever met. Find a forum or a local group to help you with the basics.
Any non-mounted horse scenario is comparable to being jumped going out of the grocery store - the horse is an external element. If you're in camp and it freaks & runs away, you can look for it later. Overall, I can't see the justification for obstaining from guns if you truly endeavor to defend yourself, especially if you're out in the wilderness alone or in a small group. This goes double if you're female; goblins just don't come in our size and they don't fight fair. Best to stay aware, use your head and have the greatest advantage possible.