This Crioulo mare is wearing a typical gaucho bridle made of tightly woven rawhide. Most closures are made with knots and buttons, rather than buckles - there is very little metal in the bridle. The reins are attached to the bit with leather straps, while the reins themselves are made of horsehair rope. The leather straps (called slobber straps in the USA) are easily replaced.
(This horse is also wearing a cotton rope halter, which makes it easy to tie her when taking a long break. The loose end of the halter rope is tied up around her neck to keep it out of the way when not in use.)
Both bridle and reins are handmade, and involve hours of work. However they are very durable, and are made with readily available materials.
What is particularly interesting to me is that this bridle design is not unlike the rawhide bridles sometimes used in the western USA. Take a look at this rawhide bridle, for example. Although it is a little fancier, with an ornamental bit and cute tassel, the braiding and button closures are identical. Or look at this one, from a recent auction. Again, slightly more ornamented, but not much.