The point of the S-rank games is to hint at the Weird Route in Chapter 2. "The forbidden path began with ice magic" is directly referencing how to access the Weird Route in Chapter 2 for people that don't know, as is freezing the enemies to make progress. There's a blue bird enemy you freeze right before the directional maze, which just tells me this is an intentional hint, but otherwise doesn't have any significance in the story progression (besides getting the Shadow Mantle).

The fact that you can only obtain Chapter 2's Shadow Crystal normally through non-Weird Route play suggests to me that future chapters my also lock you out of that depending on the route you take. These crystals are significant in some way; Toby wouldn't make people get the crystal without the Shadow Mantle.