It is possible to add dimensions to a 3D view. But only axonometric views. Camera (perspective) views don't allow any annotation.
These will continue to display when the 3D view is spun around, unlike text.
Although you can add text to a 3D view, its location is not related to any objects or workplane. So if you spin the view at all the text location no longer makes any sense.
Dimensions are drawn on the current workplane. The trick is to draw them on workplanes that make the dimensions readable in the view.
By default the current workplane is usually the floor level.
You can display the current work plane by selecting Show Workplane from the Home tab.
HINT: if you can't see the workplane it may be because it is out of your view. Zoom Extents to find it, then use the edit dots to change its size and position.
To change the current workplane use the Set Workplane command from the Home tab.
Select Pick a Plane from the dialog box.
Pick a face on an object that is in the plane you want the dimension to be in (it doesn't have to be the object being dimensioned).
But don't pick something that may be deleted, because then the workplane will disappear and your dimension will move.
Use the dimension command to add dimensions. Select the edges you want to dimension.
Change the workplane as required to place dimensions where you want them.
Selecting faces on existing elements is best practice, but if a convenient face doesn't exist you can use Reference Planes to define a workplane.
In the example illustrated sides are angled so you wouldn't want to use them for height dimensions.
Because Reference Planes aren't visible in 3D view go to a plan, section or Elevation view to draw your Reference Planes.
To set the current workplane you will need to select the reference planes in the view you created them, then switch to the 3D view to draw your dimensions.
If you move the Reference Planes (in the view you created them) the dimensions in the 3D view will move with them.
Use this approach to get the dimensions where you want them.
You can delete the Reference Planes after placing dimensions. The dimensions will still be there, but you won't be able to move the workplane any more.
The dimensions will keeping dimensioning even if you spin your 3D view, but you may need to move the dimensions to keep them readable. To prevent accidental (or intentional) changes to a view with annotation lock the view (only possible in Revit 2012 and above).