There are no mounts on a "free account" apart from the occasional mount hire for races. Well Griffon straight up costs 250 gold, but yes real money wise they’re free. There are some places in Tyria where you can rent a rollerbeetle, but other than that no, you have to buy PoF.
All mounts are tied to the Path of Fire expansion in different degrees. Even the WvW mount requires Path of Fire to be at least owned. Some also require Living World Season 4 on top of Path of Fire (2 to be precise) The only exceptions are festivals where races provide a rental mount to utilise in the area. For example you can rent one to run . 336 242 427 97 421 383 449 448