Check your state laws. In Texas we can shoot a hog with a slingshot or a Barret .50cal if we wanted to, and if you were hunting them with a bow you could darn sure carry a pistol with you. As far as licenses go, I believe in TX you still need a bottom of the line huntin license in order to hunt feral hogs/predators.
BTW, I've hunted with both .44 and .357 and would take the .44mag anyday over the .357. Elmer Keith said it best, big bullet and big hole = a lot of air in and a lot of blood out.
I think it would be interesting to load up some 230gr cast lead slugs in my .45 and try to run em up to 950fps. I think this would be as good a hog load as you could come across in .45acp. Maybe somethin to experiment with when I have the time.