In chapter 7, the animals have just suffered the loss of the windmill they have toiled over building. They believe Snowball knocked it down, but it is insinuated that the wind knocked it down as the design didn't account for thick enough walls.
The animals are feeling hopeless now that it is winter and they have to start from scratch on such an arduous project. Boxer, however, sticks to his mantra "I will work harder!" This mantra also inspires other animals to stick it out and work more tirelessly before. Clover, as always, sticks by Boxer looking up to him.
Another challenge that is facing them is this phantom Snowball which has everyone on the farm frightened. Allegedly, Snowball sneaks onto the farm and causing mischief including stealing corn, knocking over milk pails and destroying eggs. The animals cannot believe Snowball would do this.
Boxer becomes vocal about his surprise when he hears Squealer accusation that Snowball is working for Farmer Pilkington and is aiding in an attack against Animal Farm. Boxer claims that there is no way this could be when Snowball was a hero in the "Battle of Cowshed." He refuses to believe Squealer until he hears that Napoleon himself knows Snowball to have been a traitor from the beginning. Boxer changes his tune saying "If Comrade Napoleon says it, it must be right."
These are the two major challenges in chapter 7. Unless you are referring to the accusations & confessions portion of the chapter, which I wouldn't call challenges necessarily.