why were the animals easily convinced that there was a better place to go to upon their death?

No, I don't think death was part of it. Most seemed convinced that they would get to retire and live the rest of their life in relative comfort. This, however, comes to a crashing halt when they witness poor Boxer's fate,

One afternoon, a van comes to take Boxer away. It has “lettering on its side and a sly-looking man in a low-crowned bowler hat sitting on the driver’s seat.” The hopeful animals wish Boxer goodbye, but Benjamin breaks their revelry by reading the lettering on the side of the van: “Alfred Simmons, Horse Slaughterer and Glue Boiler, Willingdon. Dealer in Hides and Bone-Meal. Kennels Supplied” (123). The animals panic and try to get Boxer to escape. He tries to get out of the van, but he has grown too weak to break the door. The animals try to appeal to the horses drawing the van, but they do not understand the situation.