Is it permissible to give zakaah to feed and treat animals?

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”

[al-Tawbah 9:60]. 

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.