Just as a Jew is commanded to rest on Shabbat, so too, he is commanded to allow his animals to rest. There are two commandments that address this issue, one positive (aseh), as the Torah states (Shemot 23:12): “Six days you shall do your work, but on the seventh day you shall cease, so that your ox and your donkey may rest, and the son of your maidservant and the stranger may be refreshed”; and one negative (lo ta’aseh), as the Torah states (Shemot 20:10): “But the seventh day is a Shabbat of the Lord your God; you shall not do any melakha – you, your son or daughter, your male or female slave, or your beast, or the stranger who is within your settlements.” On Shabbat, a Jew may not lend or rent out his animal to a non-Jew unless the non-Jew agrees to allow the animal to rest (Peninei Halakha: Shabbat 20:1).
The poskim disagree about this with respect to Yom Tov. Some say that there is no mitzva to allow an animal to rest on Yom Tov. Therefore, it is permissible to rent out an animal to a non-Jew, even though he plans to use it to plow on Yom Tov. Similarly, they permit a Jew to use his animal to transport food necessary for Yom Tov, as long as it is clear to onlookers that the load will be used for Yom Tov, not for weekdays (Rema 246:3; Tosfot Yom Tov; Pri Ḥadash).
In contrast, most poskim maintain that just as there is a mitzva to allow one’s animal to rest on Shabbat, so too there is a mitzva to allow one’s animals to rest on Yom Tov. According to this approach, all laws of Yom Tov are the same as those of Shabbat, with the one explicit exception of melakhot necessary for okhel nefesh. Therefore, one may not lend or rent out his animal to a non-Jew who will work it on Yom Tov, and he may not use it to transport food necessary for Yom Tov. Even though the Jew himself is permitted to carry for Yom Tov needs, he may not use his animal to do so (SA 495:3; Maharshal; Vilna Gaon; MB 495:14).