Legal Question in Personal Injury in Iowa

Depends on what you mean by responsible.

Are you responsible for the damage to the cow? Perhaps, although this varies from state to state. Iowa does not have an open range statute so the presumption is that cattle will be fenced in. Klobnak v. Wildwood Hills tells us that the owner of an animal that roams freely is not relieved of the duty of ordinary care. Are you responsible for the damage to the vehicle you were driving? Perhaps.

No you're not responsible. Call a lawyer and sue the farmer for damages.