Unfortunately, animals today do not really have complete freedom. For example, hunting is legal for some animals and is necessary for others. Many cows, chickens, pigs, and other animals are slaughtered each day to feed Americans and every other country. They do not have a say in being killed or living, thus having no freedom.
Maybe to say them having complete freedom could be going out on a limb because most animals in the wild have many things to endure to survive like hunting for their food or the harsh weather and they are not free to roam anywhere they want without getting hunted or thrown into an animal shelter.
From most observations in the wild, I have not noticed animals having a characteristic that makes them completely free. Animals still have responsibilities to raise their young and they often participate in those tasks. Complete freedom does not exist, animals tend to have responsibilities just like humans have responsibilities. The only difference is people tend to focus one things they want, while animals only worry about what is needed.
When it comes to the issue of complete freedom and that of animals they do not have complete freedom of things like that of humans. Of course there are certain laws the are given to the protection of all sorts of animals like that of how these animals should be treated.