Welded wire fence.

This type of fence can make great horse fence, BUT it must be tall enough AND must be topped with an electric wire, or better, a wood plank, to prevent horses from "riding it down" as you can see has happened here.

The openings in the fence are small enough that hooves cannot fit through. This fence is typically used for chicken runs, goats and smaller livestock, so make sure the height of the fence is adequate.

The other problem you will run into with this type of fence used for horses, is securing the bottom of the fence to prevent horses from reaching under it, WITHOUT creating a dangerous possibility of hoof entrapment.

Barbed wire, again.

Only unsafe if you consider losing an eye a bad thing.

As the owner of a one-eyed horse (cause having nothing to do with fence issues) I can tell you it is most interesting, and I wouldn't recommend it.

Barbed wire, loose and low.

These two look like pretty nice horses, from what I can see.

Why on EARTH are they kept in too low, too loose, too dangerous fence?

Metal pipe fence.

Metal pipe fencing has many fans. Properly installed and maintained, it is considered one of the safer options.

While I'm not the biggest fan of it, I also have never used it or been at a farm where it was the primary fence type, so I'll try to reserve judgment.

As with all fence, maintenance is as important as installation. Care must be taken to prevent rust and watch for bends that could turn into cracks and exposed sharp edges.

Barbed wire over heavy gauge high tensile wire.

Oh, poor sweet face. This pony is saying, SAVE ME!

What happens when that blanket gets good and stuck on a few flesh-ripping barbs?

There ARE alternatives.