How can we be sure ice core layers are annual? What if it precipitated more often in the past?

This is a very intelligent question.

Summer snow is different than winter snow. Therefore, there are seasonal characteristics to the snowfall. These differences, as far as I understand, are caused by the dramatically different amounts of sunlight exposure. In the Summer, the Sun hardly ever sets. In the Winter, it hardly ever rises. This difference causes noticably different seasonal physical characteristics.

You are a critical thinker...I hope you are a scientist or become one.

As the first answer states, the layers show seasonal changes. With in a season there may/will be multiple snow falls. The only time a subdivision occurs is when an event puts a lot of dust/ash down on the snow and this looks different and is fairly obvious.