The fact that the planet is covered in ice and has a surface temperature of 40 below 0 suggests otherwise.
Many planet's with life were covered in ice at one point. Including Earth (ice ages).
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The ice ages most people think of didn't really affect most of the planet. Sure, the tropics were drier, but they were still tropical. There
were ice ages where the Earth was basically a big ball of ice, but there wasn't extensive flora on Earth like there was on that world.
Also, 40 below zero is the average surface temperature, not the maximum. Differences happen.
Yes, but that means that about half the planet is below 40 below, and only half is above. Without more information, we can't say with any kind of certainty except
uncertainty the amount of the world which is pleasantly warm, but it will be in the minority. And that's ignoring that such "balmy" temperatures as one or two degrees Celsius (33-34 F*) on a notable portion of the world would make it no longer ice-covered, and anyways aren't conductive to large-scale plant growth.
*In the colloquial sense, not in the actual equivalency sense.**
**I thought it would be humorous.
Oh, and the Goldilock's zone is just the zone in which there's liquid water on the surface. No life required.
True, but all life we know of requires water, and any kind of life would be impeded by 40-below temperatures. Besides, as we don't really know of how any kind of life without water would work, it's just speculation at that point. The new fluid, and there
would need to be some kind of intra- and possibly intercellular fluid, would need to be abundant, probably simple, and of course liquid at temperatures around -40. Whatever is making up the ice (so far assumed to be water) is almost certainly the most common fluid on the planet in question, and
is certainly one which freezes at the common surface temperature of the world.
Water does have some qualities which make it a great fluid for life. It's made from common elements; many substances dissolve in it; and it expands in volume as it freezes, for instance.
(Note the difference from liquid water on the surface with liquid surface water. The first can have a surface ice covering (as long as it melts sometimes))
So? I fail to see why this would be germane to our current discussion.