I did my first horseback elk hunt 2 years ago. Although not as experienced as some around here, being new let me see what you are facing.
Find out about the horses & how the horses are trained. Some quarter horses are calm animals that neck-rein & seem to make riding effortless. Other horses, especially the "half-lings" (horse/pony cross) are round pigs that break into a trot every time they think they can get away with it and shake you to death — riding them is MUCH harder on the rider. I would NOT want a "jumpy" horse under me on some of the mountain trails I've ridden over.
Most mountain horseback hunting is really commuting to the hunting area on horseback each morning, tying up, & hunting on foot all day.
Most elk shots in the mountains are inside 100 yards, but 800-1,000 yard shots may present themselves. Unless you have time to do quite a bit of practice shooting at altitude, use a ballistic program to see how your load will hit & have that data taped to your stock or inside your scope cap.
Although a .257 will take an elk given a decent broadside opportunity, a hot .30 or .338 with a controlled-expansion bullet will take elk from almost any angle. I would cary a .375 H&H before I carried a .257 on an elk hunt as these are magnificent animals that should never escape with a bullet in them that will cause a slow death & wasted animal. Use a bullet designed for penetration. (I saw a "premium" bullet fail on a near point-blank shoulder shot.) I think the .340 Weatherby may be the best all-round elk round because of it's reasonable recoil, velocity, and energy delivered to the vitals. Of your rifles, the 30-378 would definitely be my choice — if that's not too heavy for you to haul up & down mountains all day. Since you already have a .30-378, you don't NEED to buy a .338, but if you want to ... who am I to say no?
Scope choice is more of an issue than rifle for many hunters — and the one many seem to get wrong. If you are going to be hunting timber, you want a low power of no more than 3.5 or 4x, and preferably less. A lighted reticle will make your shots faster when an elk appears in the shadows. A 6.5-20 is nice to practice with & for strictly open-country hunting, but it's too much magnification if you end up hunting in timber. A 2-12x50 is probably the best all-round elk scope available. If using rented tack, be sure the scope you choose will fit the scabbard being supplied. Several people I hunted with had issues with scope size or target style turrets not fitting their scabbards. Most scabbards will not hold rifle & bipod.
A GREAT day pack really makes a lot of difference! Look for one that carries the weight on your hips & you will be thankful!! If you get an orange vest-pack you don't need a separate orange vest. (Of all the daypacks I tried, the Browning vest-pack was by far the best.)
Take a pair of trail "sneakers" along. If (when) the weather permits, these will be much easier on your legs than heavy hunting boots!
Get heavy CANVAS game bags, not the cheesecloth bags sold in the East!
Find out what size saddle-bags come with the rented horses. You need saddle bags that are big enough to hold game-bags, extra water, and extra clothing in case the weather changes during the day, and you need to be able to keep this stuff dry until you need it.
Hopefully everything will work out for you as well as it did for me. I've got a Beautiful 6x6 bull elk mounted in our dining room.
Find out about the horses & how the horses are trained. Some quarter horses are calm animals that neck-rein & seem to make riding effortless. Other horses, especially the "half-lings" (horse/pony cross) are round pigs that break into a trot every time they think they can get away with it and shake you to death — riding them is MUCH harder on the rider. I would NOT want a "jumpy" horse under me on some of the mountain trails I've ridden over.
Most mountain horseback hunting is really commuting to the hunting area on horseback each morning, tying up, & hunting on foot all day.
Most elk shots in the mountains are inside 100 yards, but 800-1,000 yard shots may present themselves. Unless you have time to do quite a bit of practice shooting at altitude, use a ballistic program to see how your load will hit & have that data taped to your stock or inside your scope cap.
Although a .257 will take an elk given a decent broadside opportunity, a hot .30 or .338 with a controlled-expansion bullet will take elk from almost any angle. I would cary a .375 H&H before I carried a .257 on an elk hunt as these are magnificent animals that should never escape with a bullet in them that will cause a slow death & wasted animal. Use a bullet designed for penetration. (I saw a "premium" bullet fail on a near point-blank shoulder shot.) I think the .340 Weatherby may be the best all-round elk round because of it's reasonable recoil, velocity, and energy delivered to the vitals. Of your rifles, the 30-378 would definitely be my choice — if that's not too heavy for you to haul up & down mountains all day. Since you already have a .30-378, you don't NEED to buy a .338, but if you want to ... who am I to say no?
Scope choice is more of an issue than rifle for many hunters — and the one many seem to get wrong. If you are going to be hunting timber, you want a low power of no more than 3.5 or 4x, and preferably less. A lighted reticle will make your shots faster when an elk appears in the shadows. A 6.5-20 is nice to practice with & for strictly open-country hunting, but it's too much magnification if you end up hunting in timber. A 2-12x50 is probably the best all-round elk scope available. If using rented tack, be sure the scope you choose will fit the scabbard being supplied. Several people I hunted with had issues with scope size or target style turrets not fitting their scabbards. Most scabbards will not hold rifle & bipod.
A GREAT day pack really makes a lot of difference! Look for one that carries the weight on your hips & you will be thankful!! If you get an orange vest-pack you don't need a separate orange vest. (Of all the daypacks I tried, the Browning vest-pack was by far the best.)
Take a pair of trail "sneakers" along. If (when) the weather permits, these will be much easier on your legs than heavy hunting boots!
Get heavy CANVAS game bags, not the cheesecloth bags sold in the East!
Find out what size saddle-bags come with the rented horses. You need saddle bags that are big enough to hold game-bags, extra water, and extra clothing in case the weather changes during the day, and you need to be able to keep this stuff dry until you need it.
Hopefully everything will work out for you as well as it did for me. I've got a Beautiful 6x6 bull elk mounted in our dining room.