If it is a specific, named hike with a defined route, we can certainly say "we did the ....". For example:
= we did the Milford Track (New Zealand)
= we did the Annapurna Circuit (Nepal)
= we did the West Coast Trail (Canada).
The verb hike could be used interchangeably, We hiked the Appalachian Trail (USA)
However, if there is no specific route, you cannot say 'did'. For instance:
≠ we did the Alps
≠ we did the Rockies.
In this case, it would be better to say we went hiking in the Pyrenees.