Is it possible to throw a couple barrels in the field with him? The more he sees them and the more they are included in everyday life, the less he is going to worry about them. Or, if you can't do that, then put treats on or near the barrels and walk him around them. Also, just ride. You might be sending him mixed signals near barrels because you expect him to freak out, and as a result he does freak out.
As for cows...I don't know what to say. Our paddocks are literally right next to a huge cow pasture, so they get over any fear they have of cows pretty quick. Your dad isn't far off the mark when he says just show the horse cows. Though no, tying the horse up wouldn't be a great idea if it's terrified of them, what you should do is just show him as many cows as possible. The more exposure, the better.
I should also point out that the less you feed into the horse's anxiety, the better it will be for everyone. I, personally, was guilty of this all the time before I realized that Tango's the type of horse that if you pretty much ignore her, she realizes that she doesn't get any special treatment when she gets upset and settles down. Acting all "Ok, it's ok horsie; you're ok, don't worry" in my experience shows the horse that there is in fact something to worry about.