If I was on my way to work at 6:30 am I hit a black cow that was loose and totaled my car, is the farmer’s insurance liable for the cost of damage to my car?

First, don't think of it as the farmer's insurance being liable--the issue is whether *the farmer* is liable. The farmer's insurance is *his* insurance--they have no obligation or duty to you. Rather, their duty is to defend the farmer from liability, and/or pay on behalf of him if he is liable. While the insurer may choose to pay voluntarily if another (you) submits a claim, they do not have to do so. So to be paid, if neither the insurer nor the farmer voluntarily pays you, you'd have to sue the farmer in court and win, proving he is liable and getting a judgment againt him.
So then the question becomes, is the farmer liable? And the answer is, he is only liable if he was negligent, or unreasonably careless. He would be negligent if he did not take reasonable steps or precautions to confine or retrain his cows, like fencing them in. But if he did take reasonable steps--such as he had the sort of fence around them that typical or reasonable farmers would use, and had the gate closed, but he cow managed to jump it without him doing anything wrong, for example--he could not be liable. The issue is therefore what precautions he took, and what factually happened.