Question: Every time I go walking or hiking, I generally spend most of my time looking down to make sure I don't step on a snake or hole or dog poop. I don't do it consciously, it just happens. Obviously, I miss out on a lot of birds and small animals up in the trees and I'd like to see how other people cope with the urge to avoid obstacles and just enjoy their surroundings.

How can I go walking and hiking without constantly looking down?

Answer: 
I find this is something I do when I can't see much of the scene in front of me at once. This is normally because I'm not far from the person in front of me. Therefore, my advice is: walk in front. Or, leave a big gap between you and the person in front of you. This is perhaps somewhat antisocial, but personally I quite like to walk alone about half the time. It lets me focus on my surroundings a bit more.
seems to me if you're hiking for distance, then watching where you're going is really important; but if you're there to see, listen, smell, etc., just slow down. Animals don't move quickly, they pause, look around, smell, listen, then move on. Birds are always looking around for threats & food. Slowing down is good- you may not cover a lot of ground, but it will be a richer experience.