Question

how does the length of day cause it to be colder during the winter?

Explanation:

In winter, days are shorter (in the Northern Hemisphere, for example). Shorter days mean the sun is up for less time, so the Earth's surface receives less solar radiation (heat from the sun) in a day. With less time to absorb heat and more time to radiate heat back into space at night, the overall temperature drops, leading to colder conditions. This relates to the Earth's axial tilt and its effect on solar insolation (incoming solar energy) over time periods, a concept in Earth science (a subfield of Natural Science, specifically Geography or Physics - related to atmospheric and solar - Earth interactions).

Answer:

In winter, shorter days mean less time for the Earth’s surface to absorb solar radiation (heat from the sun). With less heat absorbed and more time to radiate heat at night, temperatures become colder.