Whitman's definitely a favorite and an influence on me (section 20 of his "Calamus" cluster of poems, usually identified by the first line "I saw in Louisiana a live-oak growing" is one of my absolute favorite poems), and he's also a piece of queer American history. With the general disclaimer of it's always shaky to try to label historical figures with modern labels, he was very likely a gay (or bisexual or otherwise queer) man who wrote a number of poems that could be interpreted to be about gay love (or about intense male friendship, or about the love between comrades, or any number of plausible and acceptable things to his 19th century audience.) The Calamus cluster is a great place to start for a queer reading of his work, as it's the selection of his work most often pointed to as obviously gay, being largely about relationships between men (whether you want to read that as romantic and sexual or platonic, though I firmly believe it's romantic and sexual.)
The poem I took the title and both the beginning and ending quotes of this game from, section 32 of "Song of Myself", literally discusses animals and riding a horse, but couched in the same kinds of terms Whitman uses to discuss gay love ("brotherly love" in Song of Myself, compared to "the brotherhood of lovers" and "manly love" in Calamus), and I personally think there's a second reading to make about human lovers.
It's reductive, but you'll see people draw comparisons of like, if Oscar Wilde was the great gay writer of the UK in the 1800s, Whitman was the great gay writer of America at the time. It's not one-for-one, because Wilde was much more publicly gay (with all the terrible legal consequences he faced later in life), while Whitman never married and had a number of notable close male friendships, but publicly denied anything that would have been socially unacceptable at the time.
I'm the kind of person who read a lot of classics just for the sake of wanting to argue with people who were wrong about them(/using them to be shitty to other people) when I was in my teens and navigating being a gay trans man with an unsupportive family, so I picked up Whitman as one of the "foundational American poets" and went, oh shit, there's part of me in here.
I also don't feel like I can say all of this without also qualifying it with, he was a white American man living in the 1800s and was a racist and a nationalist. He wrote some really lovely things, and he also wrote and said some awful things, so read him critically. And oh god, I'm sorry I've written you an essay.
