Kitten, yes they are all one piece and attach just like any other stirrup. Here are some of the cheaper ones I have found. These don't have a full floor which I prefer. But the price isn't bad. http://www.valleyvet.com/ct_detail.h...2-00b0d0204ae5
Just google tapaderos there are all types fancy and plain expensive and reasonable.
Taken from cowboyway.com:
Hooded stirrups, also called tapaderos (or "taps") are stirrups that have a hood over the front of the stirrup that covers the front part of the rider's foot. Hooded stirrups serve several purposes: They deflect brush to help keep the rider's foot from being pulled loose from the stirrup, while also preventing the foot from being stabbed with cacti or thorns; they provide protection from weather, including to help provide extra warmth in cold weather; and they prevent the rider's foot from going through the stirrup, helping to avoid potentially serious accidents.
While riders of all types sometimes ride with hooded stirrups, they are particularly favored among working cowboys, people that ride in cold conditions, and trail riders. They are also frequently used with young riders, as many parents and riding instructors feel they are an essential safety precaution.