R. Hiyya b. Ashi said in Rab's name:
A fodder-bag may be hung around [the neck of] an animal on the Sabbath, and how much more so [may] a cushion [be placed on its back). . .
Of course, these serve two different purposes. The fodder bag allows an animal easy access to food (which makes it happy). The cushion, it is assumed, is to keep it warm.
. . .for if it [the fodder bag] is permitted there for [the animal's] pleasures how much more so here, that it [the cushion] is [to save the animal] suffering!
The fodder bag is actually debated. But the cushion/blanket is not.
An animal's pleasure does not rank against the laws of the Sabbath. But keeping an animal from suffering is a high priority.