it seems that the scientific nomenclature for families of animals in Japanese uses katakana:

• https://ja.wikipedia.org/wiki/イヌ
• https://ja.wikipedia.org/wiki/ウマ

this is confirmed by a few comments on this page: https://ja.hinative.com/questions/14614111

Basically, the kanji “犬” is used. Since “犬” is an elementary Kanji character, the hiragana “いぬ” is not often used.

The katakana “イヌ” is used in more biological contexts than “犬”.

Example:

• “Walking with a dog” 犬
• “Inu is a mammalian animal” イヌ

However, not all Japanese follow this rule. If in doubt, just write the kanji character for “dog” and you will be fine.