If a planet is far enough from its star, it will be cold, water will be frozen etc. To have plants, you'd need liquid water for at least part of the year (something like the tundra, at least.), or you'd need liquid seas where you'd have algae. If you don't have plants, you can't have all the higher order of organisms.
Winds are produced by differences in air pressure, which would be related to temperature, not to how fast the planet spins. I'm not sure how lower temperatures would affect that.
Basically, look at Earth, then stretch the polar areas towards the equator. In the depth of Antarctica, nothing lives - too cold. On the shore near the ocean, you have penguins. They live on earth, but they hunt in the water. In turn, they are also hunted in the water - there's a whole ecosystem there, with algae, krill, whales and more. All underwater, where it's warmer (marginally) and water remains liquid. In the arctic area, it's much the same - polar bears live on the ice, but hunt in the water, where you also find algae, fish, whales etc. The tundra is much more lively - plants, birds, insects, mammals - but only in summer. Once it gets too cold, everything either goes into hibernation or migrates south.
So, you can have cold habitable areas near your equator and uninhabitable large poles. You can have an ice desert with hot-spring oases. You can have the whole planet covered in ice, no liquid water, but then it wouldn't be habitable. Thing is, our cells are filled with liquid water. So if you don't have liquid water somewhere, you can't have a living cell. If you can't have a living cell, you can't have a multi-cellular organism that would produce and preserve body heat, which would allow it to live in more extreme environments.