"Hevoslinja" (Trans-Horse) is a European art project started in 2014 by Finnish artist Eero Yli-Vakkuri - according to his own words 'skilless in riding and afraid of animals' at the start.
The aim of the project was to travel 270 km / 168 miles between Helsinki and Turku in Finland, and to highlight the possibility of horse travel in modern society. Since then they've took to promoting horseback efforts in urban landscapes with several European collaborators and artists.
Yli-Vakkuri and collaborators first spent eight months practicing riding to become safely self-sufficient in saddle, and bought a Finnhorse gelding Toivottu Poika ('Awaited Son'). The route followed, as closely as possible, the old coastal royal country road of the premodern era, Kuninkaantie/Suuri Rantatie, and took 9 days.
Toivottu Poika is a very average example of his breed, standing at some 155 cm / 15.1 hh tall. The Finnhorse is a relative of for example the North-Norwegian Lyngshest breed, the Icelandic horse, the Swedish Gotlandsruss pony and the Estonian landrace horse and Tori horse breed. It is a mid-sized light draught and trotter, a sensibly realistic mediaeval country travel horse equivalent.
For more hardcore short-term treks, looking into competitive endurance riding can be helpful. Mongol Derby might be one of the most intense races, as it recreates the Chinggis Khan era postal system of swapping horses continuously over a 1000 km / 620 mile route.
By only including skilled endurance riders, keeping up a constant fast speed and swapping horses every 40 km / 25 mil, the Mongol Derby route only takes 10 days even though it's several times the length of the Trans-Horse project. This is the speed of highly organised imperial messengers with the supporting cultural infrastructure, professional marathon runners where Yli-Vakkuri and Toivottu poika were leisure hikers.
The Mongolian landrace horse is a very distant relative of the breeds above, but much lighter and smaller than the agriculturally focused modern Finnhorse - typicaly standing at 142 cm / 14 hh at most. (This would've also been common for Finnhorses before the 19th century.) What really differentiates them from Western breeds, however, is the way they're trained and raised in semi-feral herds, and it's said that while the rider may decide where the pair is headed, the horse is the one to decide how to get there.