How can I add a nose to this head without messing its shape? I am modelling a robot head that looks like this:



The shape was obtained by using very few faces starting with a square.

Now I would like to add a nose to the robot that would look more or less like this:



But instead of this screenshot which was obtained by adding a second triangle shape onto the head, I would like to model it from the head's mesh.

Here's the head in edit mode:



If I add vertical or horizontal loop cuts, the base shape of the head becomes larger where the loop cuts are added. I would like to extrude a face outwards where the middle of the face is, but there is no face there, and I only know how to add one by adding loop cuts.

It is important for me not to lose the almost spherical curvature of the chin and sides and top of the head... And obviously I would like not to apply the Sub Surf modifier because I am trying to keep the model light and easy to edit...
Your mesh is so "Low Poly" that every nev vertex will interact with the subsurf algorithm, modifying the overall shape; but you need some extra vertices for the nose; so the solution is: RETOPOlogizing.
Create a new object (I.E. a plane), set all the little buttons circled in red and start moving and extruding vertices: every time you move a vertex it will snap onto the surface underneath. So you will be able to put how many vertices you want, exactly where you want, without modifying your shape. Useful also for good deformation topology, if intended to be animated.