The word "horny" is rather colloquial and can have different meanings. Primarily, it can refer to being sexually aroused. Some synonyms in this context could be:
aroused: This is a more neutral and somewhat less vulgar term. For example, "She was aroused by his touch." It simply indicates a state of sexual excitement.
lustful: Implies a strong desire or craving, often sexual. For instance, "He looked at her with lustful eyes." It suggests a more intense and perhaps less controlled form of sexual longing.
lecherous: This has a negative connotation and indicates an excessive or immoral sexual desire. For example, "The old man had a lecherous look on his face." It implies a kind of lasciviousness or depravity.
If "horny" is used in the sense of having a hard or rough texture like horn, synonyms could be:
coriaceous: This is a more technical term meaning having a tough, leathery texture. For example, "The insect's shell was coriaceous."
sclerous: Referring to something hard or indurated. For instance, "The plant had sclerous tissues."
It's important to note that "horny" is a rather informal and sometimes vulgar word, so its synonyms should be used carefully depending on the context and audience.