Are the animals free under Napoleon's rule? In which ways have they become slaves in Animal Farm by George Orwell?

The animals are certainly not free under Napoleon's rule.
As an allegory about Russian Communism, George Orwell's Animal Farm illustrates the ousting of the ideologue Leon Trotsky and the brutal dictatorship of the tyrant Josef Stalin. This ousting occurs with the tyrant Napoleon's calculated destruction of the windmill and his chasing off Snowball, the ideologue.
Named after Napoleon Bonaparte, who became as great a despot as the aristocrats whom he overthrew, Napoleon becomes power-hungry. He has trained dogs to protect him and to attack dissenters. His propagandist is Squealer, who speaks to them with circumlocution and sophistry. His loyalty to Napoleon, as well as his lack of any conscience, accompanied by his rhetorical skills, forms the ideal propagandist for any tyrant. 
Napoleon eventually has the Ten Commandments changed to a single one:
                    ALL ANIMALS ARE EQUAL        BUT SOME ANIMALS ARE MORE EQUAL THAN OTHERS.
He also has the sheep chant, "Four legs good; two legs bad." This chant drowns out any type of intelligent debate. Later on, the chant is altered to "Four legs good, two legs better."
The manipulation of language and the commandments keeps the animals from any independent thought. Further, this removal of independent thought certainly takes away freedom. So, the animals stop protesting, especially when they are attacked by the dogs. Like Stalin, Napoleon becomes dictatorial rather than democratic, and the animals are made to work more, they are fed less, and the rules have changed. If someone protests, he or she is liable to be chased and bitten by the dogs, so the animals becomes inhibited. Or, if an animal is no longer useful, he may be killed as in the example of the Boxer, the loyal believer, who is tricked into climbing into a truck that takes him to the glue factory.