After all the Christmas decorations get put away for next year, and the Christmas tree eventually gets undressed from all its ornaments and retired to the compost pile or green waste, all the pretty seasonal potted plants remain.
Some will bloom, or at least maintain their current bloom, for months. Some might eventually get planted out in the garden. Others might stay potted in the home.
Poinsettias are the epitome of seasonal potted plants for Christmas. Their flashy red bracts last a very long time, even after the tiny yellow flowers are gone. Some are pink, white, pale yellow, peachy, marbled or spotted. They can be grown as foliar houseplants, but will not likely bloom next Christmas. If protected from frost in the garden, they get tall and lanky, and bloom in January.
Christmas cactus is an excellent potted plant either indoors or out where protected from frost. The pendulous growth cascades nicely from a hanging pot. It blooms in phases, but does not stick to a tight schedule.
Amaryllis should also stay potted only because it does not do well in the garden over winter. Foliage that develops after bloom will die back next autumn before bloom next winter.
Holly and azalea can be planted directly into the garden where appropriate. Azalea will probably look shabby until it gets new growth.
Cyclamen is a perennial in the garden, but dies back over summer. It just might come back with a surprise in autumn.
Paperwhite narcissus is perennial, too, but exhausts its resources on bloom, so takes a year or more to recover before blooming again.
Small living Christmas trees are more variable than they seem. Rosemary can either be kept potted and shorn, or planted into the garden and allowed to grow wild or into another form. Dwarf Alberta spruce can likewise stay potted or get planted into the garden, but needs no shearing.
Both rosemary and dwarf Alberta spruce will want larger pots as they grow.
Italian stone pine and Canary Island pine grow into large shady trees, so should only be planted into spacious landscapes that can accommodate them.