The phenomenon you're referring to, where the sky appears very bright at night during winter, is known as "winter bright nights" or "winter noctilucent clouds." These occurrences are observed in high-latitude regions, typically between latitudes 50° and 70° in both the Northern and Southern Hemispheres.
Winter bright nights are caused by the presence of noctilucent clouds, which are thin, high-altitude clouds composed of ice crystals. These clouds form in the mesosphere, the third layer of the Earth's atmosphere, at an altitude of about 76 to 85 kilometers (47 to 53 miles) above the Earth's surface.
Noctilucent clouds become visible during astronomical twilight, which is the period after sunset or before sunrise when the Sun is between 12 and 18 degrees below the horizon. At this time, the lower levels of the atmosphere are in darkness, while the high-altitude noctilucent clouds catch the sunlight, reflecting its rays towards the Earth.
The reason why winter bright nights are more commonly observed in winter months is due to specific atmospheric conditions. In the mesosphere, the temperatures drop to extremely cold levels during winter, reaching around -120 degrees Celsius (-184 degrees Fahrenheit). These low temperatures create favorable conditions for the formation of ice crystals, which make up the noctilucent clouds.
The ice crystals in noctilucent clouds scatter sunlight, creating a glowing effect that illuminates the night sky. The clouds' high altitude allows them to catch sunlight even when it's well below the horizon for observers on the ground, resulting in a bright appearance during the dark winter nights.
It's worth noting that winter bright nights are relatively rare phenomena and are most commonly observed in polar regions or regions with high latitudes, where the angle of the Sun below the horizon remains low even during nighttime.