Praise be to Allah.
Allah, may He be exalted, has defined the categories to which obligatory zakaah may be given, and has not left them to the reasoning or choice of the person who is giving zakaah. Allah says (interpretation of the meaning):
“As-Sadaqaat (here it means Zakaah) are only for the Fuqaraa’ (poor), and Al‑Masaakeen (the poor) and those employed to collect (the funds); and to attract the hearts of those who have been inclined (towards Islam); and to free the captives; and for those in debt; and for Allaah’s Cause (i.e. for Mujaahidoon — those fighting in a holy battle), and for the wayfarer (a traveller who is cut off from everything); a duty imposed by Allaah. And Allaah is All-Knower, All-Wise”
For more details on the eight categories mentioned in the verse, please see the answer to question no. 46209
Animals, in general, are not one of the categories of zakaah recipients that Allah has listed for His slaves, whether it is for feeding them, treating them or anything else.
But that restriction applies to obligatory zakaah, so it is not permissible to give any zakaah for the care of animals. As for feeding animals, treating them or being kind to them, that comes under the heading of voluntary charity.
It was narrated that Jaabir (may Allah be pleased with him) said: The Messenger of Allaah (blessings and peace of Allah be upon him) said: “There is no Muslim who plants something but whatever is eaten of it is charity for him, and whatever is stolen from it is charity for him, and whatever the wild animals eat from it is charity for him, and whatever the birds eat from it is charity for him; no one takes anything from it but it will be charity for him.”
Narrated by Muslim (1552); al-Bukhaari (2220) narrated a similar hadeeth from Anas.
It was narrated from Abu Hurayrah (may Allah be pleased with him) that the Messenger of Allaah (blessings and peace of Allah be upon him) said: “Whilst a man was walking on the road, he became very thirsty. He found a well so he went down into it and drank, then he came out. There he saw a dog that was panting and biting the ground out of thirst. The man said: this dog is feeling the same thirst that I felt. So he went back down into the well and filled his shoe with water, then he held it in his mouth until he climbed back up, and he gave the water to the dog. Allaah appreciated (his action) and forgave him.” They said: O Messenger of Allaah, will we have reward with regard to these animals? He said: “In every living thing there is reward.”
Narrated by al-Bukhaari (2363) and Muslim (2244)
There is no doubt that such actions, if they are done in the appropriate place and time, are praiseworthy, but it is not part of Islam, nor is it wise or rational, for a person to be preoccupied with doing that, or setting up charities to help with it at the time when there are humans, and indeed his brothers in Islam, who are dying of hunger, homeless, sick, and have no money with which to relieve their hunger, treat their sickness or find shelter. What is required of the Muslim is to strive to meet his brothers’ needs, even if they are far away from him, even if they are in another country, if he is able to reach them himself or send his money to them. Allah will help a person so long as he helps his brother.
And Allah knows best.