The animals group themselves by species, the dogs together, the pigs together, the hens and pigeons together, suggesting from the start that the idea that "all animals are equal" will have to overcome some obstacles based on "class." The dogs and the pigs sit near each other and near the front, showing their connected and dominant positions in the hierarchy. Boxer and Clover are characterized from the start as caring, as they worry that they will step on some small animal they don't see in the straw. The sheep and the cows lie behind the pigs, showing that they will follow the pigs' lead later on. Moses, the raven, stays outside. He represents the clergy, the voice that pacifies the animals and upholds the current status quo by telling them stories of a wonderful afterlife, and like the real clergy in Russia, will not take part in the revolution/rebellion.
The dogs' instinctively going after the rats does not bode well. The animals, to successfully implement their ideals of Animalism, will need to overcome many natural tendencies and will need good leadership to do this. Old Major can provide that leadership, though he dies before the Rebellion, but it is equally possible for a more cynical leader to exploit the natural tendencies of the animals, such as the dogs, for his own gain, which is what Napoleon will do.
As Old Major gets up on the platform to speak, the other animals enter. The order of the animals shows a sort of ranking that is not apparent in chapter one, but will become clearer as the book progresses. Let me give you the text.
"Before long the other animals began to arrive and make themselves comfortable after their different fashions. First came the three dogs, Bluebell, Jessie, and Pincher, and then the pigs, who settled down in the straw immediately in front of the platform. The hens perched themselves on the window-sills, the pigeons fluttered up to the rafters, the sheep and cows lay down behind the pigs and began to chew the cud. The two cart-horses, Boxer and Clover, came in together, walking very slowly and setting down their vast hairy hoofs with great care lest there should be some small animal concealed in the straw..."
"All the animals were now present except Moses, the tame raven, who slept on a perch behind the back door. When Major saw that they had all made themselves comfortable and were waiting attentively, he cleared his throat and began."
The dogs come first, but they do not sit in the seats of honor. They come first because they will be the "muscle" of the pigs later. They will make sure that the pigs reign supreme.
The pigs do have the seats of honor. They settle down right in front of the platform. This signifies that they will rule the farm. They are the smartest and so have control.
The hens are on the windowsills - presumably because they can fly. There is probably little significance here.
Then the horses come. They are powerful, but they are cautious and kind, which they prove in the story. Finally, there is mention of Moses, the raven. This, too, is important, because Moses is an outsider and continues to be one. So, in a short section, we read of the hierarchy of what will later be known as Animal Farm.
Significantly, Old Major speaks on "a sort of raised platform" above the other animals, immediately undermining by virtue of his physical position the equality about which he will speak. In addition, it is also important that even though at first there is some order to the gathering, pigs in one place, ducks in another and so on, very quickly that order collapses as "the dogs suddenly chase the rats," giving lie to the comradeship Old Major speaks about so eloquently.
The pigs are at the front, foreshadowing their status as the more "important" and superior of the animals. Clover is watching over the lost ducklings, and the other animals are pushing and struggling to get a place.