It was left deliberately ambiguous in the initial write up and I've had players do both.
In fact some groups living the events in present tense but editing them as if they were a story, some telling the whole journey as if it were a story, and one in particular who were telling tall stories at camp on an otherwise uneventful crossing.
You can kinda have it either way, I tend to find players will follow whoever leads in but they tend to surprise me too