I've been speaking with a local HVAC contractor for doing the installation in my house.  The first floor of my home is ICF, and I have a dormered second floor that is stick built.  He's never worked with installing HVAC in an ICF house before. 

I've already had EnergyWise do the heat loss calcs for my house, and I've selected some equipment.  Other than that, I really am a newbie when it comes to HVAC.  Is it correct you should only run heat and cold air return ducts through the interior studded spaces?  I have a large open living space that is my living room/dining room and kitchen.  Is it OK to run ducts on exterior ICF walls?

Is your question that you are having to chase ductwork vertical on the interior of the icf wall? Yes?

Yes, that's my question.  I haven't seen the design of what my HVAC guy wants to do, but he mentioned how he could channel ducts into the ICF foam walls.

This sounds as if it is a framing question only. I would suggest not removing foam. Breaks the thermal barrier. Foam is only 2.5" deep at max on most forms. I am assuming the walls are built otherwise this is a definite no.

Have the heating guy reroute the ductwork!

Yes, you can place the duct on the icf wall and then cover in dw, but cutting the duct into the wall is asking for trouble, for more than one reason. Now it you want to run a perimeter duct in a soffit, that may be an architectural feature created by a consistant sized soffit; placing a lone duct up the side of the wall would like like hel.