I recently started a new game and am going the route of the mage. Before visiting High Hrothgar I decided I wanted to do the Winterhold questline to get some spells and levels under my belt. The first part of this involved demonstrating a ward spell. I personally found it annoying that when I put up my defense, Lydia drew her weapons while the trainer threw a spell at me. I found this detracted from my experience so I am thinking of telling her to go cool her heels while I do this questline.
*Will I regret not bringing a companion with me on the Winterhold questline (either for inventory space or tough encounters?
*Are there other questlines in the game that having a follower really doesn't make sense?
Maybe I'm way off base here and I've never played far in my previous playthroughs, but I can imagine there are stealth missions where you probably wouldn't want/need a follower. Then again, maybe their awkwardness is just something you've got to put up with.