The Freezing Band is a planet-encircling region of land on the tidally-locked planet called Oristania. Through tidal locking to its home star, Oristania has a adopted an extremely contrasting set of environments in its regions, ranging from ground-melting hots to air-freezing colds. One side of the planet continually faces its star as it orbits around, while the opposite side faces eternal darkness and a lack of direct sunlight. Only a very thin band between these two regions supports living conditions, and is further divided into distinct areas.
One of these areas is the Freezing Band, a strip on the Habitable Zone bordering the dark side of Oristania. Where the middle of the Habitable Zone sees its star just on the edge of the horizon, the Freezing Band can only witness the light shining over the distance. Very little of this eternal glint is capable of warming the Freezing Band, and temperatures vary little throughout the year beyond random shifts between 200 Kelvin (-100 F, -73 C) and 230 K (-45 F, -43 C). The virtual void created by the dark side of Oristania draws in warm air rising on the dark side, cools it, and returns it back towards the light side. Wind speeds are a continually fierce force then, with biting colds sweeping the ground towards the light side. Warm air above would cool further down the path, saving much of the Freezing Band from facing an eternal blizzard.
The entirety of the Freezing Band is essentially a planet-wide glacier, with its surface slowly inching closer to the Habitable Zone and melting as it reached it. Organisms actually living in the Freezing Band, however, would not enjoy the benefit of these liquid waters. Life here would be dominated only by those who could manage a strict water retention rate, low heat dissipation, and a modem of securing water (heating the ice) with little energy expenditure. Most creatures here would likely sport a form of brown fat across the entirety of there body to induce heat generation at the cost of futile energy cycling. As the cold requires much more out of an organism's metabolism than does cooling in the face of heat, organisms would need a modem of energy conservation to survive.
For example, one such organism would utilize the benefits of undergoing periodic torpor to save energy otherwise used for heating their internal temperatures (it would thus be an endotherm, ectotherms would more likely utilize cryoprotectants to survive). Stationary during torpor, however, it would need to keep itself protected from would-be predators. This organism (let's call it an Ice Breaker) would bury itself in tube of ice surrounded by a warming secretion. Much like a trap door spider on Earth, it'd remain inactive (in this case, undergoing torpor), until a prey item passed by. Torpor is an arduous hours-long metabolic process on Earth, and so this organism would likely have to display some strange chemical pathways to get in and out of torpor expediently. Arising from torpor in seconds, the Ice Breaker would reach out and snap up the prey item before beginning the digestion process, likely utilizing the breakdown processes excess heat to help keep warm.
Plant-like life would find difficulty living in the Freezing Band, but not impossible. Certain tree-like organisms could live within the Freezing Band, closer to the Habitable Zone (and ultimately form a sort of taiga). The freezing lower winds would have to be protected against by extensive layers of insulating bark, whilst the upper regions would attempt to extend far into the sky, reaching the warmer, moisture-saturated airs above. The ice it sits within would only be easily melted in areas with underground thermal activity. These trees would get their water by soaking up melted ice resting above volcanic regions in the Freezing Band. Tough fleshy plants could surface through the ice as well, making up loose patches of vegetation for sparse herbivores to feed on.
Intense hibernators could survive tissue freezing utilizing cryoprotectants and anti-freeze chemicals in their haemolymph, possibly waiting out periods of blizzards or intense colds in the Freezing Band (as Oristania orbits, the distance between it and the star would affect global temperatures; as it distanced itself, portions of the Freezing Band would drop in temperature for months at a time). Others would migrate closer to the more temperate Habitable Zone.