It is as you identified a walking axe. Tony K is pretty accurate with his summary of its uses. The only comment I have to make is that walking poles are OK but if you are are in the Alps trying to self arrest on a 1,000 foot slide toward the valley floor after you've fallen traversing a couloir. Which one do you think will do the job? The poles or the axe? If you are going to do steep walking in snow, get an axe and learn how to use it. The short handled axes are used mainly for more technical, and vertical patches of ice. Having said all that, mixed route mountaineering is great fun if hard. If you get the chance in this country, enjoy it, if not go for a summer in the Alps, with a guide/instruction of course.
Technical data. Spiky end = Pick. Other end = Adze. Handle = Shaft. Loop that goes round your wrist = Leash