No, like I said, not having a melee weapon is enough
StoryWeaver:
The Second Floor so far:
Corridor of barrack entrances and special rooms (including the one that the party rested in before). At the end of the hallway is a door that leads to more of the building (unexplored)
Syrio:
think we'll go here next, please
As they return to their resting spot, the group sees the floor being dry, the frozen surface a distant memory to the place.
They go to the door on the other end of the corridor. Upon opening up the door, the group sees a large room, a little sparse in details. In that room is several doors, one left and two to the right. In the centre of the room, there is a partially enclosed, spiraling staircase. Not the most utilitarian tool for ascension, which stands out from the general "form over function" attitude to most of the monastery.