Serious Question- I only play a few hours during the week, and I have not tried this yet. Can I hop onto my horse and freely explore Tamriel or is there really an invisible wall that won't let me through certain zones?
There's no invisible walls, not exactly. The closest there is are the slaughterfish in the water, but even then I wouldn't want to swim from Wayrest to Sentinel anyway.
There's a bit more of a difficulty spike instead. If you're around level 8 or so and you head to the next zone, that's fine and everything, but you'll definitely have to tread carefully so that you don't get yourself killed by the mobs there. You could still take the quests there, and depending on the amount of combat you might be able to complete some of them, but no, you can't go anywhere and do anything right from the get-go-get-go.
There's plenty of stuff to explore in each zone, so I don't mind the slight linearity of it. I honestly think it benefits the game, actually.
going to the next zone very early is that yes you would be able to do quests, follow other players around you could probably do most.
this would level you up fast as you would get lots of xp from the quests however if you do it for all zones you would have an gap so you is level 40 while you need 50 to start with the VR content and you either had to do PvP a lot, go back and do the now very easy quests or grind up to 50