There are a number of science fiction games that can describe worlds in scientifically accurate terms. GURPS Space or related suppliments was extensively researched and can give a resonably believable results.

The 'world generation' takes into account luminosity of the sun, albedo of the planet, density of the atmosphere, percentage of ocean coverage, etc. If the sun is warm enough any ice blowing out from the night side would melt. That would provide at least some liquid water, maybe enough for extensive oceans.

You map is nice, and I agree the projection centered on the 'twilight band' makes more sense, if you think the inhabitants are biased towards the areas they live. You would have to do an overlay of an ice-cap across the night side areas.