Technically, trumpets are not horns. Horns have conical bores. Brass instruments have a cylindrical bores and a flare at the end. The flare of a brass instrument is mostly for projection. The conical bore of a horn is primarily for timbre.
You're right that trumpets have cylindrical bores, but that's not a universal characteristic of brass instruments. For example, cornets and euphoniums have conical bores, yet they are brass instruments; their cylindrical-bore counterparts are trumpets and baritones, respectively.