Only a few species of Mesembryanthemum are hardy, like ice plant Mesembryanthemum crystallinum. But this plant cannot withstand more than about -5 °C to -10 °C, which may make overwintering difficult.

Look at the label of your ice plant when you buy it. To be on the safe side, overwinter a perennial plant in a frost-free room in the apartment or in the conservatory. Limit watering and refrain from fertilizer until spring.
It may be that your purchase is an annual ice plant, in which case overwintering is usually not worthwhile. But you can harvest the seeds and grow them on the windowsill from February or try overwintering cuttings. So you don't have to buy new plants in the spring.
The essentials in brief:
- not all varieties hardy
- Label should provide information
- as a precaution winter frost-free
tips
If you would like to try hibernation, then choose a frost-free winter quarters.