Snakes will almost always strike at what is closest to them. A walking stick is your best protection. Hold it out in front of you. Don't try to provoke the snake. A lot of people, when they find them, are more than a little curious, and just can't leave it alone. That's when the trouble starts. Most rattlesnake bites occur because of peoples inability to just walk away. BTW: The best snake bite remedy is a set of car keys. Get in the car and go to a hospital.
Large cats are not always that elusive. I have a cousin in Reno that I visited for a few days. She told me that if I wanted to go jogging or biking, stay off the road up against the foothills. There had been several joggers attacked while running by. Think about it. You're just a giant running mouse.
Sometimes I carry a .38, but it is more for plinking while we are out. I do have it loaded with snakeshot while we are on the trail, not that it would help much. If they decide to strike it's too late to draw, as they are lightning fast.
I did know someone that a pistol came in handy for though. They were out on some old ranch property, and when they opened the door to the outhouse, there he was...ready. The guy shot him, and then the girls were able to use it.