A certain portion of the United States has cold winters. Butterflies that fly in these areas spend the winter in at least one stage of their lifecycle--egg, larva, chrysalis, and/or adult. This website does not address how to overwinter adult butterflies; but it does address how to overwinter eggs, larvae, and/or pupae.
To keep butterfly immatures alive during the winter, certain strategies and equipment are helpful. The common element to any strategy addresses three basic concepts:
Most eggs, many larvae, and few pupae will either dessicate (insufficient humidity) or mold (too much humidity/insufficient airflow) if kept in the refrigerator for a period of time.
Nevertheless, using the refrigerator can be an effective overwintering technique if butterfly immatures are exposed to the right amount of humidity and provided with airflow. Your strategy in caring for immatures wintered in the refrigerator follows the following immature groups based upon sensitivity:
1. Pupae and Mature Last Instar Larvae. Keep in container with screen top. Mist spray every 14 days or so during the front end of winter; every 7 days or so on the back end. Adjust according to how immatures respond to humidity in their natural habitat. This group of immatures are LEAST sensitive to dessication and mold.
2.   Caterpillars that overwinter as half-grown larvae such as many brushfoot butterflies, some sulphurs, some satyrids, etc. need more care than pupae and mature last instar larvae. They require mist spraying at least every four days; but not so much that creates mold. Some trial and error is needed to fine tune your own strategy. Overwintering these immatures outside in a protected terrarium might be more advisable.
3.   Butterfly eggs, larvae that overwinter as unfed first instar, or Limenitis hibernacula: This group is the most sensitive to desiccation on the one hand or mold on the other. If you overwinter any immatures of some Speyeria, Boloria, Cercyonis, etc, you need to pay very close to them.
The greater fritillaries (Speyeria spp.) and some lesser fritillaris (Boloria spp.) overwinter as unfed first instars and can die easily during the winter. This occurs because these small larvae are extremely susceptible to desiccation on the one hand (insufficient humidity or airflow) or mold on the other hand (too much humidity with insufficient airflow.)
The following presentation provides a step-by-step tutorial of one successful strategy of how to keep Speyeria unfed first instar larvae alive for up to 180 days in the refrigerator.
Special thanks to Abe Homan for providing this detailed information as well as photographs.
If you’re interested in overwintering butterfly early stages on your own property, you need to make sure that your setup has some degree of consistent humidity, protection from predators, including mice, and a reasonable amount of airflow. The photographs below show containers placed inside glass terrariums with screen lids with the terrariums themselves protected by a wooden box and lid. This setup offers less airflow than the Alpine Method of overwintering; but is suitable for those stages of immatures which are less sensitive to dessication and mold as a result of decreased airflow. Those immature stages include pupae as well as mature fifth instars. This technique does not work as well with Nymphalid half-grown larvae, ova, and especially unfed first instar Cercyonis and Speyeria larvae. This technique works only where cold winter temperatures exist. If you live in the sunbelt, using your refrigerator to winter immatures is recommended.
Utah butterfly collector Jacque Wolfe devised the alpine overwintering technique which satisfies the three important criteria of overwintering—that butterfly eggs, caterpillars, and pupae be provided airflow, humidity, and protection. Immatures are placed inside squat tubs that have tens of thousands of needle holes. These "holy containers" are placed inside either a screen-riveted five gallon bucket or a heavy duty screen cage. This setup is found in a high elevation Utah mountain bog where plenty of winter snow provides more or less constant humidity.
This method especially accommodates sensitive immatures such as Lycaenid ova, Limenitis hibernacula, Melitaeinae half-grown larvae, and especially unfed Speyeria and Cercyonis first instar larvae.
Please remember that this technique is more principle-driven than method-driven. In other words, Jacque was innovative in deciding to overwinter sensitive immatures in holy squat tubs, hanging in screened five gallon buckets over alpine bogs in the tops of the mountains of Utah. However, you yourself can create a setup that satisfies the same criteria with a completely different methodology. Simply remember the three main criteria, that immatures need humidity (to avoid dessication), airflow (to avoid mold), and protection from predators.