Great advice from everyone. I'm printing out this thread and filing it.
I'd break the problem/solution down into pieces:
-1- No neighbor has any right whatsoever telling you where you can or cannot put your mares on your own property. The only exception I can think of to this is if the neighbor's well is on your property - he has a right to not have poo in his well. Doesn't sound like that's an issue. Keep telling yourself that: it's your land, not your neighbor's. It is better to annoy others than to let others annoy you (when you're right).
-2- Like stated many times, contact the powers-that-be and find out exactly what the laws in your area are: Fence out, fence in, fence set-backs, special requirements for keeping stallions, etc. Study it well so you know exactly who's in the right and wrong before you do or say anything at all. Make sure whatever you end up doing keeps you in the right. It will prevent a potential lawsuit. These neighbors sound like the suing type. Knowing your rights always makes any verbal confrontation easier to handle as well.
-3- Rather than arguing with the neighbor and trying to force him to do something (ie taller fence, etc), I personally would just bite the bullet and do whatever fencing I felt was necessary to keep my horses in and that stallion out. I would want to use my land, and not have to worry about anything, and I would not leave that up to someone else. Once that's taken care of, they can complain all they want. Block their phone #.
-4- As satisfying as it would be to use barbed wire of other hazardous fencing materials to create a moat, I wouldn't do it. The neighbor would deserve the aftermath. The horse wouldn't. I think if he got tangled and shredded himself on the barbed wire, the neighbor would learn their lesson. However, if you love horses, you'd probably feel really awful for that stallion. Remember that your own horses could pull some unforeseen antics and end up in that wire too. Probably in the middle of the night - because that's what they seem to do.
Legally, you probably can't take down the current fence to build a new one further in, since you have joint ownership of it. If it's legal, I'd take that puppy down and build my own fence on my side. Otherwise I'd put a strand of electric wire 6' up on the current fence and send the neighbor the bill for half the fencing and half the power-bill and put my mares wherever I wanted. If ordinances require 6' fencing for stallions, I'd send him the whole bill. He may not pay it, but it sends a message and puts you on the offense.
What is the current fencing? Is it fancy expensive stuff? How long is it? Is it something you can afford to abandon and rebuild? Is it sturdy so it can withstand mares and stallions on either side?