Middle English trampen, to walk heavily, from Middle Low German.
derivation from www.dictionary.com
Peculiar New Zealand etymological variant on the activity of trekking, hiking or bushwalking.
To go tramping in New Zealand usually required that you carry all your needs in your backpack, as historically there was no network of bush huts available to spend the night in. Possibly, for the duration of the trip you become a 'tramp'.
Ignoring political issues, the bulk of New Zealands most recent colonists were lower to middle class Britons who would generally know nothing of leisure activities like rambling in the hills, so to go out with all your possessions in a backpack was to lower your class even further and become homeless.
New Zealand has extensive network of National Parks with established tracks. Some world renowned one are The Milford Track and The Routeburn Track. Lots of people come to New Zealand for the purpose of tramping but end up trumping.