Just to sidetrack for a moment:
There are people who claim an ice axe is never required in the Whites, and my position is that they're fools. There are definitely locations on popular hikes where an unarrested fall will result in serious injury or death. Not many, and they're very specific, but they do exist. Locations where I like to have mine in hand: snowfields on Washington and in the northern Presidentials, the snowfield on Lafayette, the slide on Wildcat A, the ice flow on Kinsman Ridge Trail between Cannon and Coppermine Col, and any time the conditions are packed/icy such that a slip is going to result in an uncontrolled slide (I recall a day on KRT in Kinsman Glade where only the crampon points would penetrate the surface; a stumble and fall would have been ... bad ... without self-arrest).
That said, the common rule is "better without it than untrained with it" because if you don't know what you're doing, you could easily injure or kill yourself with the axe.
PS - it's not just the axe to be conscious of when performing self-arrest. Get those feet up in the air! Snagging a crampon while sliding is a great way to break a leg, tumble uncontrollably, and die.
PPS - axe technique is not just self-arrest. There's also planting the axe into the snow while hiking. That's something that I was taught in a Tucks snowfield, but I have not needed in the Whites ever since. Only carry and be ready for self-arrest.
