Do as I did .... Play it as anything but "the way it was supposed to be played "
With most modern mods Morrowind can become something else, and though I know a lot of people here hate on it for the clunky combat and quest structure it is one of those games that can become almost anything you need from an RPG.
I use it mostly these days to immerse myself in an alien fantasy setting and personally am an avid modder for it.
The RAW experience is truly grueling and I have to admit it. You losing stamina is a matter of being low level and low skilled, it gets much better as you level and then negligible after 5 or 6 if you invest a bit in Alchemy or stamina related skills.
To move around I recommend you use the silt striders or boats at the start.
Also you might reconsider using some mods that speed up stamina regen and even health/magicka as well, several out there, but what I do is just invest a bit in Alchemy and make some simple stamina regen potions. If you start as a mage it will be even worse for you as magicka does not regen naturally
TLDR? Just mod it a bit to your liking, the original experience is good but honestly it deters people from enjoying this wonderful game that people hate for the sake of joining the hate train as they got too used to Skyrim.