They don't begin laying eggs again until spring. Monarchs are the only species of butterfly that participate in a true migration. They migrate south, then when spring arrives, return northward to reproduce. The location of the overwintering grounds in central Mexico was only discovered about 25 years ago. They do not become mixed up and unable to migrate as some extreme sources would propose.
Monarchs stop and nectar along their journey south.
Monarchs are the only species that truly migrate - that is the original southward migrants make the return trip to the north again in the spring. But, there are some species of butterflies that head south to spend the winter months in warmer climates. The painted lady is one example. One species, the mourning cloak, is known for its unusual ability to hibernate as an adult. The adult butterflies will find crevices in tree bark, siding of houses, etc. where they will remain sheltered from the most severe winter weather.