Snares are not catching the wild animals you see running around. They have a chance each day of catching either a rabbit or chicken, and when they do you will see a little bag hanging on it. When you "check the snare" you will get a little rabbit or chicken item in your inventory and the snare disappears (one use).
As long as they aren't too close to any buildings you should be fine. Sometimes it will take a few days for the snares to "catch" something. They don't have to be in the woods, along trails, or anything like that. I have used them successfully on dirt, fertile soil and forest soil. They might not work on rock or sand or clay, but never tried. Oh, and spacing doesn't matter either - I usually make a line of them next to each other to make them easier to check.
(Note animal traps work completely differently - they will only trigger when an animal or player walks over them. They do damage and root them for a short time.)