Water. I wouldn't want to be desperate enough to drink out of the stock tanks. All kinds of gross creepy crawly things in there. Like these things that look like miniature horseshoe crabs with long rat-like tails. Yuck!
I would guess a lighter or matches would also be good, just in case it's winter and I get lost. And a GPS to hopefully prevent that from happening.
I don't worry much about the wildlife. I saw my first bear this year, and it was when we were still in the truck. Never saw a cougar, although my neighbors have. I worry more about the two-legged predators, but I don't carry a gun, just a pocket knife.
Maybe it's a false sense of security, but I feel very safe on a horse. They are an extra set of eyes to spot humans and animals. And if I do need to get away in a hurry, it will be a lot quicker on horseback than on foot. I guess that sums it up. I feel safer on horseback than on foot.