Ballistics by the inch is my go to for answering these questions. here is a link for the .357 ballistics.
http://www.ballisticsbytheinch.com/357mag.html
I carry the S&W .357 J frame, similar sized barrel for EDC. So I have contemplated this question extensively. My advice would be to be to practice a ton with .38 ammunition at the range. Practice until you have mastery of the gun and you know what it and you can do. I'm talking about hundreds of rounds. Then practice some more from your holster.
Once you and your weapon are comfortable, Again in my opinion, any of the heavier personal defense rounds will be more than you need for any threat you will find (short of Brown Bears) I personally carry golden saber rounds, but would/will go to the buffalo bore round next purchase cycle.
The recoil and flash/bang of any of the "big boy" personal defense rounds is mighty, but when faced with a threat I really dont think you would even notice.
The threat you are most likely to face in the outdoors are two legged jackasses, probably close to your truck at the trail head. Although cats are apparently starting to be a bigger issue. All of the training, big assed bullets and the like will be completely worthless unless you can quickly and safely access your loaded and ready to go firearm and bring it to bare on the threat. Again back to my first statement, PRACTICE.
All of this is worthless unless you can get to the firearm. In a pocket of your pack is a complete waste of your time, unloaded is just as bad, a quality holster where your shooting hand can access the weapon, in a crisis, is what you should be trying to achieve.
The only time I have had to deploy and use my handgun in the backcountry was on a rattlesnake last fishing season. The nasty serpent was in a choke point along the river where my dog and wife had already passed. I didnt feel comfortable leaving it alone with the need for all of us to have to come back through the choke point. The .357 golden saber was more than enough to deal with that particular threat...