These small sized horses are called ponies (or pony). These adorable ponies are quite rare (in many parts of the world) as they cannot be used for commercial purposes.
I found these in many parts of Netherlands used as pets. They just keep grazing all the time.. and its so good to watch them
Many breeds of these ponies are found all over the world. Here is a list of them with good details about ponies.
http://en.wikipedia.org/wiki/Pony