According to the knot, the peony is the 7th most popular wedding flower. Probably because of their beautiful lush blooms, fragrance and most importantly, their demand. Unlike roses, which have a long growing season and therefore can be found throughout the year, peonies have an EXTREMELY short growing season (late spring to early summer). While not available for winter weddings, they can be imported for a fall wedding and are available in a range of pinks/purples (from the lightest almost white to the deep purple-y pinks), as well as lush red and classic white.
Like I mentioned before, the growing season of a peony is very very short- usually only about 7 weeks. This makes the price of the bloom incredibly expensive (especially if you are having to import them in their "off season"). This doesn't mean that you can't enjoy peonies though! Think about single bud vases in the windows of your venue, or mixing other flowers in with peonies for a lush, beautiful, and way more affordable bouquet or centerpiece. Or maybe you'll carry a bouquet of peonies and your bridesmaids will carry a mix or different (but still complimenting) blooms. More often than not, your florist will completely understand that you don't want to blow your entire budget on flowers and will work with you to make your vision happen within your budget. If not, you might want to research other florists!