They don't go far. During the warm months they wander over about 20 acres. They are protected by our livestock guardian dogs. During the winter they stay within about 50' of the nesting area. You might try building a sun room like this:
http://sugarmtnfarm.com/2006/01/31/chicken-sunroom-how-to/
In the winter ours prefer staying in there to going out on the snow even though they can. In the sun room they have hay to stand on and it is warm. At night they go into the coop.
I'm surprised that an inch or two of snow is grounding out your fence. It takes a foot or two to make much difference on ours. It might be that your energizer is too low powered. I recommend at least 2.5 joules, preferably more if it is powering a lot of load. I use 6 and 15 joule energizers. You might also want to dry clipping the leads to the bottom couple of wires. See:
http://sugarmtnfarm.com/2008/06/12/poultry-netting-for-pigs/
For predators I would suggest having a guardian dog. Ours eat predators. It's a dog eat coyote world out there.