On a separate matter, please also don't assume that carrying an ice axe and wearing crampons will necessarily lessen the consequence of a slip. They may help prevent a slip (asusming you know how to use them) but unless you know how to self arrest an axe could be likened to a glorified walking pole. Even knowing how to self arrest may not help you if you quickly gather speed down an icy slope. Practice, practice, practice (without crampons to start) before you get yourself on high-consequence terrain to get a feel for how difficult it will be! This experience doesn't come with the sales receipt!