Is it possible an ice line from pole to pole in a tidally locked Earth-like moon?

I am aware that there are a lot of answers explaining the fundamentals of a tidally locked "Earth-like" moon around a giant gas planet. For example this one:
Habitable moon of a gas giant: working out the sizes and distances

However, my question is related to a very particular side-effect of the tidal-locking: Imagine this guy standing in the side of the Earth-like moon that is always facing to the giant gas planet, as shown in the picture (I show there 4 positions of the moon around the planet). The drawing is obviously not to scale. It is just to explain the idea graphically:

That face of the moon where the little guy is standing (as you can notice) will almost always be in the twilight and will never have the sun directly perpendicular to the surface. So, my question is:
Is it valid to assume that there will be an ice line (or at least a very very cold zone forever in Winter) in the meridian directly pointing to the planet?
I mean: something like this picture:

posted about 6 years ago

Carlos Zamora‭

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