Lingon: I'm pretty sure, the light side very close to the rim would have ice. What I wanted to say with the north pole comparison is, that: The north pole in summer has very long days of very low standing sun. That the sun goes down for a few hours (except the very middle of summer some few days) evens out the fact, that at midday it's a good bit higher than the horizon (light hits at a blunter angle thus more heat per area). This way I think the situation exactly at the rim is comparable to earth's poles. (It would be better, if earth had no axial tilt but it has to do. I guess you can imagine, that the poles would not suddenly melt if the earth would turn a bit to rotate in the solar system disk.)

Now, how far day-wards the frost-zone would go is a different question. And of course, if your planet has a warmer average temperature (more greenhouse effect, stronger sun, anything,...), than obviously the rim can be ice free or the border of ice.

Yes, the dark side would be one huge high pressure zone and the light side one huge low pressure zone.


Pixie: I think you are overestimating the gravity fueled movement. I think the water would flow towards the day-side, too, to replace the water that evaporates there.
Let's see, the hottest places on earth get around 55°C warm on their all-time hottest days. Now, if the sun would not be directly overhead at the beginning and end of summer, this would probably be even warmer. Maybe 70°C? Much more important of course is, that the sun never goes down and never shines from a low angle, thus the light energy per area should be 4 times as high per time than on the hottest day. Since hot bodies give away energy faster than not so hot once, this does not fourfold the temperature but it should still be a huge impact easily increasing the temperature to 150 or 200°C. Water boils and evaporates (As you move away from the point where the sun is directly overhead, this should fall quite quickly, so the costal lines seam possible to me, though I'd expect the innermost shores in the day zone to be boiling hot.)

And I definitly agree with the bad weather. The hot side evaporates a lot of water, hot air can carry more water than cold air, thus as the air cools down on its way towards the dark side, their will be lots of rain. And since this rain falls from a rather high altitute, some of that will probably turn to snow and hail