Type the name of the horse or pony you are looking for next to 'Name' and press the search button. You can use % as a wildcard. E.g. If you enter STAR% you will find all horses and ponies whose name starts with STAR. If you use %STAR% you will find all horses and ponies with STAR somewhere in their name.
If you want to find all horses and ponies for a particular owner or breeder, just enter their name in the space provided. This can also have wildcards.