WHY THERE ARE NO HORSES IN MORROWIND:
The Charioter is a sign representing a horse, but there is an obvious lack of horses inside Morrowind. This is a sad fact when compared to the predecessor Daggerfall, which had horse travel as a main in-game mechanic.
But why is there an absence of horses in this game? The reason might surprise you

Answer:The Hardware and Engine were not prepared.

Bethesda was entering the 3D market, where games were transitioning from 2D sprites to 3D sprites. This required a significant amount of effort and time consumption because they also needed to focus on modeling in-game characters. Overall, the 3D nature of Morrowind was, at the time, a risky but successful experiment in changing the genre of Elder Scrolls into a more open-world exploration game. This meant that some things would be sacrificed in this journey. The map was smaller but somehow bigger and more well-made with more content inside. Daggerfall's map was larger, but most of the time, it was empty.
Due to hardware limitations, the map size was reduced. To compensate for that, Bethesda put more effort into making the content inside the game good. This is the main reason for the absence of horses because Morrowind was Bethesda's first 3D game, and trying to implement a horse in an engine designed for 2D games was a task even bigger and harder. Creating a living vehicle (a horse) was much more challenging to implement in an experimental game like Morrowind.
These challenges prevented Bethesda from attempting something risky like implementing horses because they didn't know how they could make it work at the time. Horses were only implemented in the future, firstly introduced in Oblivion and then mastered in Skyrim. Overall, Morrowind was Bethesda's first real experience with 3D games, and they decided to play it safe, not venturing too far into programming something they had never tried before.