What you are talking about is armored or metal clad cable. Those posts look to be spaced pretty far apart. I don't think I'd be drilling holes though those structural posts. Also, if you were trying to run the wire horizontally, you'd need a way to support the wire between posts. There are minimum staple distances to be adhered to for code reasons. It also might depend on what type of insulation you are planning to do, and what type of wall covering you are planning on. If it were me though, I'd just do all my wiring surface mounted in EMT conduit after the walls are insulated and covered.
Brian