They won't have the same kind of concept of it but they definitely have fear (and live with it a lot of the time). Look at a deer and how cautious they are or even a hamster, which won't walk across the middle of a room but is jumpy and sticks to the edges, cautiously creeping around.
We don't have a 100% foolproof way of telling how much pain they experience. A lot of it is guesswork. But yes they don't have the same cognitive abilities as a human (although that's our biased POV). If we are just talking about physical pain with no emotional component (which isn't all of pain) then they could experience that part in similar ways - I think so, anyway.