I too spend a lot of time on my horse. Not cross country time, but 1000+ miles a year, sometimes twice that.
To me Glocks (or any semi auto with no thumb safety) and horses don't mix, so that's out. Outside that there's lots of choices. I'll only say if it were me I'd carry a SA revolver of the compact versions now available in a good medium to high ride pancake holster so it could be covered with an untucked shirt. Or, your SP101 should serve you just fine as my Taurus M605 has me, although I have switched mostly to the SR40c.
Another thing to consider is the potential problems of carrying a firearm on the horse, not on you. Any kind of accident and a lot of situations (there are a LOT of potential scenarios) would lead to you not having control of your firearm(s) if they are attached to the horse, not you. Especially bad in highly populated areas. Easy pickins for a thief or the attention of LEO. Also, when traveling through towns you may attract some onlookers. All may not be well wishers just waiting for you to go into the store. I'd say if you're going to hunt, do it once you get out west and have some one send you a rifle or buy one there.
It would be neat to follow your adventure. Are you going to be reporting your progress on line?
Best wishes either way.