Both those plants are hardy perennials and can live outdoors in your zone. Their natural lifestyle is to grow leaves and flowers in the spring and summer and to die back to a base of leaves or a root in the winter. Next spring they will grow back up again. They can continue this cycle for several years.

Most indoor plants hail from tropical areas where they are used to even temps and light levels all year round. That's why they can survive in our homes. Hardy perennials require a winter rest and trying to keep them growing all year round indoors will weaken them. You will be killing them with misplaced kindness.

They don't need to be 'buried' in Winter but they do need to be planted in the ground. This forum is quite quiet so for further help with hardy perennials you could try asking on the Perennial forum here on GW.