In Chapter 1, what are the different ways in which the animals behave as they come into the barn and what does this tell us about them?

The different animals reveal their personalities as they enter the barn. Let’s start with Old Major, who’s already sitting in the barn when the scene begins.
1. Old Major sits in a comfortable way that shows he is calm, kind, dignified, and very much in charge:

Major was already ensconced on his bed of straw, under a lantern which hung from a beam. He was twelve years old and had lately grown rather stout, but he was still a majestic-looking pig, with a wise and benevolent appearance in spite of the fact that his tushes had never been cut.

2. The three dogs and the pigs come in first and sit down right in front of Old Major, which shows that they are prompt and obedient:

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.

3. The hens and pigeons come in and settle themselves in the places where they are most comfortable, showing that they are prompt and attentive, but perhaps less eager than the dogs and pigs:

The hens perched themselves on the window-sills, the pigeons fluttered up to the rafters…

4. The sheep and cows come stretch themselves out comfortably behind the pigs and chew their cud. This shows that, like the birds, they are perhaps ready to listen and follow orders, but perhaps they care a bit more about eating than doing so, and they aren’t quite as excited as the dogs or pigs:

… the sheep and cows lay down behind the pigs and began to chew the cud.

5. The horses come in as a pair, showing their friendship, and they sit down carefully so that they don’t hurt any of the tiny animals, showing their conscientious manners:

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.

In particular, the narrator tells us directly that although the horse Boxer looks and is rather stupid, he’s actually very respected on the farm because of his good character and his hard work:

A white stripe down his nose gave him a somewhat stupid appearance, and in fact he was not of first-rate intelligence, but he was universally respected for his steadiness of character and tremendous powers of work.

6. Muriel, the goat, and Benjamin, the donkey come in next, and although we don’t see how they enter or where they sit, the narrator tells us directly that Benjamin has a bad attitude, that he’s very negative and serious, and that somehow he was still very good friends with Boxer:

Benjamin was the oldest animal on the farm, and the worst tempered. He seldom talked, and when he did, it was usually to make some cynical remark—for instance, he would say that God had given him a tail to keep the flies off, but that he would sooner have had no tail and no flies. Alone among the animals on the farm he never laughed. If asked why, he would say that he saw nothing to laugh at. Nevertheless, without openly admitting it, he was devoted to Boxer; the two of them usually spent their Sundays together in the small paddock beyond the orchard, grazing side by side and never speaking.

7. The ducklings wander in helplessly next, then get cozy and fall asleep, revealing how clueless and useless they are:

The two horses had just lain down when a brood of ducklings, which had lost their mother, filed into the barn, cheeping feebly and wandering from side to side to find some place where they would not be trodden on. Clover made a sort of wall round them with her great foreleg, and the ducklings nestled down inside it and promptly fell asleep.

8. Mollie, the mare, comes “mincing daintily in,” meaning she prances in, showing off. Right away she sits down in the front of the room and shows off her mane, which is decorated with fancy ribbons. She’s also enjoying a sugary treat. So, we can see that she’s self-indulgent, a show-off, someone who loves attention:

At the last moment Mollie, the foolish, pretty white mare who drew Mr. Jones’s trap, came mincing daintily in, chewing at a lump of sugar. She took a place near the front and began flirting her white mane, hoping to draw attention to the red ribbons it was plaited with.

9. The last animal to come in is the cat, whose name we aren’t told; she looks for a warm place to sleep and ignores absolutely everything being discussed. She purrs, enjoying herself. So, we know that she is utterly uninterested in what Old Major has to say, nor does she care much about the farm as a whole.

Last of all came the cat, who looked round, as usual, for the warmest place, and finally squeezed herself in between Boxer and Clover; there she purred contentedly throughout Major’s speech without listening to a word of what he was saying.

10. Finally, one animal didn’t enter the barn at all. Moses, the raven, instead remains sleeping outside of the barn, revealing his total indifference to the other farm animals:

All the animals were now present except Moses, the tame raven, who slept on a perch behind the back door.