The horn of an ox underlies this metaphor (cf. Deuteronomy 33:17; 1 Kings 22:11; Psalm 92:10) which symbolizes military strength and victory (cf. Psalm 89:17, Psalm 89:24; Lamentations 2:17).1 In this case it refers to Hannah's dignity,2 her visible vindication before Peninnah and the wider society, and her lasting strength through her offspring.3
1 And Hannah prayed and said, “My heart exults in the LORD; my horn is exalted in the LORD. My mouth derides my enemies, because I rejoice in your salvation.