Would it be possible for someone to carry a shield, a sword, a bow, and an arrow all at once? Or would carrying a greatsword, a bow, and an arrow be more realisitic. Light armor of course.

Unlike the way the game shows it, bows are often carried unstrung, strapped on to whatever other gear one is carrying. So I don't think it makes a lot of difference. As for the shield, it was common to have a strap on it, called a "guige," to allow it to hang over the shoulder when using a two-handed weapon like a bow.

What's unrealistic is how fast the game allows us to switch weapons.

Yeah, less realistic than casting spells, dragons, and absorbing said dragon's souls.

Yeah, I'm worried about us, believing all that stuff.

So technically a warrior could carry all 4 then?

You forgot talking dogs.