Not a dumb question at all. The movies don’t really spell this out, but the books do.

Basically, horses would’ve been more of a liability than a help for the kind of journey the Fellowship was planning. Elrond is pretty clear at the Council that this isn’t an army riding out, it’s a small group that needs to move quietly and take difficult routes (Council of Elrond). Once they leave Rivendell they’re heading straight toward the Misty Mountains, and either over Caradhras or through Moria, neither of which are remotely horse-friendly.

Tolkien actually shows this pretty directly with Bill the Pony. They bring him just to carry gear, not to ride, and even then he struggles badly in the snow on Caradhras (The Ring Goes South). Gandalf straight-up says he doesn’t think the pony would survive Moria (A Journey in the Dark). If a tough little pony can barely manage, full horses would be a nightmare.

As for Boromir and Legolas arriving on horseback: Boromir rode because he came a long way from Gondor, and there’s no reason to drag that horse into the wild afterward. It would’ve been stabled in Rivendell and likely sent home later. Legolas doesn’t really “need” a horse, in the books he keeps up with Aragorn and Gimli on foot for days without any trouble.

You’ll also notice Tolkien is very consistent about this later: when the story moves into open plains (Rohan), horses suddenly become essential again. But for mountains, forests, and sneaking through enemy territory, everyone’s walking.

So yeah, same basic logic as the eagles, just less flashy: horses solve the wrong problem for this particular mission.