Before it comes up about liability, each state has different laws. On roads in Idaho, an open-range state, livestock have the right of way: if an animal is hit and killed by a vehicle, the driver is liable for the price of the animal and for the repair for the damage to the vehicle.
In some other states with open range, if you do not want cattle on your property, it is your responsibility to erect a fence to keep them out.
East of Cody, WY I had to wait for a large flock of sheep to meander across the road. They were not in a hurry and it must have taken 30 minutes for the entire flock to reach the other side so that I could continue on my way.