Siman 536
Presented here for study, not as a practical ruling. The Shulchan Aruch rules by Sephardi custom, the Rema's glosses by Ashkenazi custom, and the Kitzur follows Ashkenazi custom. For a practical question, ask your rabbi.
א מִי שֶׁצָּרִיךְ לִרְכֹּב בַּמּוֹעֵד לְטַיֵּל אוֹ לְצֹרֶךְ הַמּוֹעֵד, וְלֹא נִסָה לָלֶכֶת בְּרַגְלָיו, יָכוֹל לִטֹּל צִפֹּרְנֵי הַסוּס וּלְתַקֵּן בְּרַגְלָיו וְהָאֻכָּף וְהָרֶסֶן וְכָל צָרְכֵי רְכִיבָה, וּבִלְבַד שֶׁלֹּא יְכַוֵּן מְלַאכְתּוֹ בַּמּוֹעֵד. הַגָּה: וּמֻתָּר לִרְכֹּב בַּמּוֹעֵד אֲפִלּוּ מֵעִיר לְעִיר, אֲפִלּוּ בְּחִנָּם, וְכֵן נָהֲגוּ; אֶלָּא שֶׁאָסוּר לְתַקֵּן כָּל צָרְכֵי הָרְכִיבָה אִם אֵינוֹ רוֹכֵב לְצֹרֶךְ אוֹ לְטַיֵּל (בֵּית יוֹסֵף).
1 All Animal Needs Can Be Done on Chol Hamoed, 4 Seifim: One who needs to ride on an animal to travel for pleasure or for a holliday need and cannot walk is permitted to trim the horse's hoofs, to fix its horseshoes, saddle, and bridle, and to do any other activity necessary for riding. This assumes that one did not plan to do this work on the holiday. Rema: It is permitted to ride on Chol Hamoed even from city to city and even for no reason, and this is the practice. However, it is prohibited to do activities necessary for riding if one rides neither for a holiday need nor for travel for pleasure (Beit Yosef).
ב מֻתָּר לִסְרֹק הַסוּס כְּדֵי לְיַפּוֹתוֹ.
2 It is permitted to brush a horse to make it prettier.
ג אֵין מַרְבִּיעִין בְּהֵמָה בַּמּוֹעֵד, אֲבָל מַקִּיזִין לָהּ דָּם, וְאֵין מוֹנְעִין מִמֶּנָּה כָּל רְפוּאָה, אֲפִלּוּ אִם יֵשׁ בָּהּ מְלָאכָה.
3 We do not breed animals on the holiday, but we do draw blood. We do not withhold anything medical, even if it involves labor.
ד אֵין מוֹשִׁיבִין תַּרְנְגֹלֶת עַל הַבֵּיצִים לְגַדֵּל אֶפְרוֹחִים; וְאִם הוֹשִׁיבָהּ קֹדֶם הַמּוֹעֵד וּבָרְחָה מֵעֲלֵיהֶם, יָכוֹל לְהַחְזִירָהּ, אֲבָל אָסוּר לְהוֹשִׁיב אַחֶרֶת אֲפִלּוּ מֵתָה הָרִאשׁוֹנָה (בֵּית יוֹסֵף); וְהוּא שֶׁיִּהְיֶה לוֹ בְּתוֹךְ ג' יָמִים לַבְּרִיחָה.
4 We do not sit a hen on eggs to grow chicks. If she was placed before the holiday and ran away, one can return her (but it is forbidden to put a different one there, even if the first one died) (Beit Yosef). This is only the case when it is within three days of her running away.