Unless it's a nursing mare, it is not in a horse's gene pool to share food.
There is always a dominant horse. Their mindset is, and always will be, eat for survival; regardless of the hundreds and hundreds of years they have been domesticated.
Even though you are the Alpha when you're within your herd, all bets are off once you leave. Humans don't count for anything once we're back in the house or headed out the drive to our jobs.
How big is your paddock? You have an awful lot of livestock in a "paddock", which is generally inferred as being a small area.
Since the words "hay pile" were used, we all assume that's it - one pile of hay, on the ground. A ground that will get churled and muddy when it rains.
When I throw hay in the winter for my four horses (not in the paddock either), there's always at least 8 piles of hay. Horses are grazers/movers by nature - they will play Musical Chairs with the hay piles until the everybody finally settles down to eat.
Eight piles for four horses (spread out in a straight line) assures everybody is eating what they want.
That being said, if your paddock is small, my suggestion is to invest in six hay holders that can be placed above the ground. Make sure to keep them where the goats and calf can reach them.
They will eliminate some waste (especially when it gets muddy), and everybody gets to eat.
Honestly, I hope a paddock environment is temporary and that pasture fence is being built. To repeat myself, six pieces of livestock in a paddock with one hay pile is way too much; especially when they are three different species
Granted it would be great if they all get along. But, I promise you in the end, ONE of the two horses is going to dominate over the hay because it is slowly making up it's mind it is not going to be the one to starve to death
I am sorry if I sound harsh but there's not a very PC way to say this particular truth