There does seem to be a side preference with animals, though it can be harder to determine if they don't do things to make it apparent. I've spent a lot of time staring at sheep while they chew their cud and stare back at me, and noticed things like they all seem to rotate their jaw in the same direction as they chew their cud, and have a tendency to turn their head one way more than the other, such as when lying down (this was important when I'd be inserting cannulas into their jugular vein for long term blood sampling or drug delivery; put it on the wrong side, and it gets kinked and becomes useless whenever they lie down...since the purpose was to sample without disturbing them from their normal activities, we needed to ensure we could sample even if the sheep laid down). They also paw the ground to dig a little indentation in their bedding before lying down, so they exhibit "handedness" in doing that, and when mating, both sheep and goats kick up with their forelegs at the flank of a potential mate, and there is usually a side preference in doing that as well (helpful to know when you have to lead away the female a male is trying to mate with to know which side to stand on to avoid getting stuck in the middle and being kicked yourself).