Welcome to the forums.
Are you sleeping in a position where you put pressure on your stomach? Are you sleeping in your clothes or pajamas of some kind? If you are, it could be that maybe some stitches in your clothes or blankets are making an indentation on your skin when you are sleeping on them and your body is applying pressure on them. Whenever I wake up I usually have red or white lines all over my arms from where I slept on a blanket and it made a pattern on my skin.
Maybe you could just be seeing your veins, but those are usually a blue/light blue color.
Sounds strange.... what position do you sleep in? On your stomach? Do you think there's any difference in you sleep position with and without a snack? Do you go to sleep quicker or slower, or no difference when you have a late snack?
I'm just suggesting some things you can examine to help find the cause. My guess is the lines are due to external physical pressure on your chest area during the night. When you get up whatever the presser was is gone, you are up and on your feet.