Is the feed, water, and medicine for livestock counted as charity (sadaqah)?

Providing water and food to your owned animals is obligatory for you, and you will be rewarded for it, even if you do not actively intend to seek reward. As Al-Baji said, "There is a reward for every living being with a moist liver," and this is general for all animals.

Good deeds are of two types: 1. Necessary deeds (whose benefit does not extend to others): One is rewarded for them if performed with an intention, even if it is merely the intention to fulfill an obligation. 2. Transcendent acts of worship (from which others benefit): One is rewarded for them due to the benefit reaped by others, even if one did not have an intention when performing them, such as removing a harmful object from the road or planting a tree from which an animal benefits.

Thus, removing a harmful object from the road has a transcendent benefit, and a person is rewarded for it even if they had no specific intention.