These small immobile dolls are called Frozen Charlottes, and they date from the late 1800s - early 1920s. Sometimes called bathing dolls, they were usually crudely made of china.
The tiniest in my collection measures just 1 inch tall, while the largest is 3 1/2. The first doll is atypically made of clay, while the third doll is also unusual, as it appears to be a boy, and has a small thatch of hair and gold painted boots.
Frozen Charlottes look great in groups or clustered in arrangements, and also make good dollies for larger dolls to hold.