Generally succulents are able to be left outdoors during winter (in their natural surroundings many succulents are exposed to very low temperatures), however when extreme temperatures, beyond that which the plant has evolved to cope with are experienced, the plant will begin to suffer.
Damage to the tissue of most succulents is sustained when temperatures dip below freezing for a sustained period of time. There are species that can handle these conditions but as a rule of thumb think of 35F as the threshold.
To reduce the risk of plant damage, during colder months many Etsy sellers encourage the inclusion of heat packs in amongst parcels containing live succulents.