I keep horses off the pasture for about 9 hours a day. That seems to keep them from becoming overweight. It works out to either while I'm at my day job, or overnight. But, regardless of my schedule, it seems to be adequate and appropriate for the horses in my care.
She would most likely respect a white tape electric wire to separate the pasture. If you can swing it, it may help keep the whole acreage from getting overused, overgrazed in spots, and encourage the grazing of less desirable, but still non-harmful weeds.
I have not used grazing muzzles because it requires that the horse wear a halter and I prefer to not leave a horse haltered at pasture. But, if that is what I needed to do for a time, I certainly would use one. Just haven't had to.
Most horses do well staying in a run, or run and stall combo. In some urban areas, that's all they ever get and they do alright. But, if you notice excessive signs of boredom there are many, many gadgets on the market to entertain a stalled horse.
Goats can be tough to keep in a pasture. Special "sheep wire" fencing is often required. As much as I like goats, keeping one (or some) in a pasture isn't a challenge I would choose.
Most people object to barbed wire because if a horse does reach through with a hoof and leg there is a likelihood of it suffering a worse injury, due to the barbs, than if the wire was smooth.