Cake eggs: temperature has a technological role

In a few sentences

In brief

In a cake made by creaming butter, cold eggs can firm up some of the fat and make a uniform mixture harder to achieve.

Useful to know

In a cake made by creaming butter, cold eggs can firm up some of the fat and make a uniform mixture harder to achieve. King Arthur explains why some recipes explicitly call for eggs at room temperature. [1]

Follow the particular instruction, since other batters deliberately use cold ingredients. Prepare only the amount needed rather than turning a preparation requirement into a storage rule. Egg temperature and the order of addition are separate from the number of eggs. Equal quantities do not guarantee the same intermediate texture.

Sources

For further detail and to check the information:

[1] King Arthur Baking — do eggs used in baking really need to be at room temperature ↗