I was leading the pack string out of the Trinity Alps Wilderness area one year and tied up at the pack station at the Hobo Gulch Trailhead. The folks that ran the pack station there had a little Australian Shepherd that had been bitten on the face by a Western rattlesnake. This little dog weighed about 50 pounds and its head had swollen to about the size of a volleyball. They slipped four Tylenol down its throat and hoped for the best. The little guy laid around the pack station for a few days but then recovered completely.
You have to remember that a snake's venom is programmed to kill things like rats and mice, not dogs, and from most of the stories I've heard, most dogs seem to recover.
Not so for horses, however. Horses are usually bitten when they're out grazing and accidentally bump into one and are bitten on the nose. Their nostrils swell up and inasmuch as horses can't breathe through their mouths like a dog, they die from suffocation, not from the venom.
Anyway, it sounds like your friend's dog has a real good chance of making it.