The differences between mix and mixture are subtle.
A mix of something is often descriptive of the make-up or components of a mixture:
The castle was built from a mix of sand and water.
A mixture, on the other hand, is the thing that is mixed:
The cake mixture is often a mix of eggs, flour, and oil.
There is a lot of wiggle room in usage and the distinction of when to use one or another is fuzzy. A general rule of thumb is to use mix when naming the individual parts, and mixture to describe the whole.
In the examples you gave, I think both would be acceptable, because you are either talking about a mix of hiking and camping that make up the trip, or the trip's "mixture" of hiking and camping.