You know you don't have to shoot full bore 44 mag ammo in a 44 magnum revolver. You can load it down or buy 44 special loads. Most of my handgun hunting has been done with a 255 grain cast gas checked lead .429 bullet pushed at 1250 fps and that's a very comfortable load to shoot and very accurate. Slightly hot 44 special loads deliver more energy than the 357 and give less felt recoil also.
The 44 magnum 5.5 inch Ruger Redhawk I carried and hunted with for years. This went in a nylon shoulder holster and was both comfortable to shoot and carry.
For a woods carry gun I agree with Wyosongdog. I carry a stainless four inch 34 ounce Taurus 41 mag Tracker. It weighs the same as a Smith & Wesson K frame 357 (34 ounces) and carries much more energy than a 357 with factory loads. Of the 19 black bear I killed with a 44 or 41 mag with hardcast lead bullets I simply could not tell much difference in killing power. These all were run at around 1250 fps. A 255 grain for the 44 and a 230 grain in the 41 mag.
The 4 inch Ported 41 mag Taurus Tracker. At 34 ounces this gun goes comfortably on a belt or in a shoulder holster and is near as light as my stainless 22 Rossi J frame size revolver.
I carried and shot and big game hunted several 44 mags over the years and the 44 or 41 mag is by far the best in the woods for killing power compared to the 357. I spent five years in Alaska and the rest of my 60 plus years in Idaho. Had one grizzly encounter in Alaska that ended up with a dead grizzle at the hands of a Smith 29 44 mag.
Another consideration is weight. You can comfortable carry a heavy handgun in a shoulder holster. Once that gun gets above 38-40 ounces it's to heavy to carry on a belt holster.
As a ccw carrier I use a Taurus 38 special ultra-light snubby that's carried in an Uncle Mike's pocket holster in a front jeans pocket. It simply goes with me everywhere all the time.
Here's my ccw gun. Less than 20 ounces and with it in an Uncle Mikes pocket holster it just disappears inside a front jeans pocket, leaves no outline and is always there. It's the top one. The second is the small frame 22 and the bottom is the 41 mag tracker to give you an idea of comparative sizes.
That little gun is designed for people protection and carries Speer Plus P 125 grain gold dots. If I'm going to the woods, fishing, hunting or picking huckleberries or mushrooms a the 41 mag tracker goes on a belt or in a comfortable shoulder holster with me. It's loaded with Lee's 210 grain tumble lube cast bullets at 1050 fps. That load has killed several black bear and is very comfortable to shoot.
I've ran into very few situations in the woods where a sidearm was necessary in a self defense role against an animal, but those few times I sure was glad I had the 44 or 41 instead of a 357. It's hard to beat horsepower.
I also agree that if you are new to shooting handguns get a 22 rimfire in a simular platform as your centerfire carry gun and learn to shoot it. Those skills will carry over to all the handguns you shoot and good shooting skills are the bottom line regardless of what you carry in the woods. The little Rossi or a Smith J frame plinker is exceptionally accurate, fun to shoot and the extremely low recoil helps learn handgun accuracy.
Another consideration is cost. You can afford to learn to shoot a 22. Learning to shoot well with a 357, 41 or 44 magnum is near impossible not only from a cost point of view, but managing recoil and learning to be accurate even from a 357 for a beginner is simply one of the silliest thoughts I've heard of. This from being a handgun instructor for lots of years.
One more thought. An ultra-light 357 is far harder to shoot than a medium weight 41 or 44 magnum. If you don't believe that go to a range and rent and shoot one of the Smith scandium framed 357's.
Got a friend whom has one and he delights in letting folks that haven't fired one shoot it. He makes them shoot it on his lawn simply because most folks end up dropping it on the first shot. It's really not much good for more than a conversion piece. Of the dozen or so folks that have shot this lightweight 357 including me I've yet to see one whom wanted a second try at it.
The bottom line here is if you need a gun then any gun is better than none, be it a 22, 38, 357 or 500 Smith & Wesson.
