This poem is an ‘Acrostic’. An acrostic is a poem (or other form of writing) in which the first letter (or syllable, or word) of each line (or paragraph, or any other recurring feature in the text) spells out a word, message or the alphabet.
In this poem, the first letter letter in each line when joined together form the word “HORSE”. And the first speaker is trying to ask the second one for a ride together.
Canticle is a hymn or chant, typically with a biblical text, forming a regular part of a church service. This is an ACROSTIC poem. First alphabet of each line joined together from a word. In this case, it is the title of the poem.