What is an electric company's liability regarding a downed utility pole?

Most likely the overhead wire on your family's land is there as a result of a recorded utility easement. To confirm, you should order a preliminary report from a title company to confirm. As to liability for the death of several cows caused by the downed utility pole owned by the electric company, I would make a claim for the value of the lost cows and see what happens.

If the claim is denied by the electrical company, you will need to evaluate whether the pursuit of any legal action is worthwhile with an attorney experienced in real estate and agricultural law. You will need to prove negligence by the utility company and damages. Since the pole fell over during a storm, the utility company would have the defense of "act of nature" to any claim unless it knew that there was a pre-existing problem with the pole and did nothing to rectify it.

Possibly your family may have an insurance policy to cover the loss of the cows to look into.