The concept/goal of Journey

Besides the minimalist aesthetic, the game is incredibly short, so presumably they expected people to complete most, if not all, of it in a single sitting and thus did not provide a means to "save and quit". Instead, Journey auto-saves at the end of each "level" and there is no option to save at will or more frequently. This is similar to other thatgamecompany titles like flOw and Flower.

So you don't have to worry about making sure you quit a specific way: just quit using the PlayStation XMB.

The only winning move is not to play. Watch their patrols and hug the walls where their searchlights don't go as often. Once you get spotted by the search light, they will likely catch you unless you're in the last section where you're surfing down the middle as fast as possible. It is possible to get through it without losing the part of your scarf, but it's mostly stealth.

In the snowy area, you should utilize cover and only move out from under cover when no snakes are approaching.