Ok...so I'm actually relatively new to TES. I'm used to games where magic users are a clearly distinct class and it isn't something you can pick up at a community class from the YMCA. In game there is some suggestion that magic isn't hugely widespread, but from a gameplay standpoint it definitely seems that way. In both Skyrim and Oblivion (not sure about the previous titles) you start out as someone who can just do that. What does lore say regarding Tamriel's denizens' natural inherent magical prowess or lack thereof?

Well, magic seems rather common and the lack of common usage is a result of distrust and lack of cultural value. Everyone on TES can learn, but few have what it takes to master a school of magic.

According the Lore, some Races are more in tune with Magic than others (Breton or High Elves) and most races have some inherent magical ability. In the world of Nirn, it seems that being a magician is like being a chef, anyone can do it if they want to learn how, but not everyone is going to be great at it and some are going to be naturals.

For the most part, you won't run into magic that much.

The in game feel of magic seems to be mistrus.

magic is the math of TES, each and every person can learn and the vast majority have some basic knowledge of it but a lot of people hate it