Plant the rose cuttings at any point throughout the year. Some people like to plant them during the cool months, while others wait until the early summer. Rose cuttings should be able to grow during any season. However, keep in mind that they'll need to be constantly watered, so if you plant them during the summer or live in a hot climate, they're going to dry out faster. For this reason, the rainy season might be your best option.
Although miniature roses have always been grown on their own roots since the 1950's when they were first introduced, Ralph Moore of Sequoia Nursery in Visalia, CA, near Fresno, offered many of the larger roses on own-root along with his vast selection of minis. His Playgirl floribunda has always been sold by Ralph as own-root cuttings in 4-inch pots, as well as a good assortment of other own-root floribundas and old garden roses. Unfortunately, Mr. Moore is now deceased and his nursery is closed.
There will be disappointments along the way, when many rose seeds fail to germinate, or perhaps they do germinate, only to die several weeks later from damp-off disease. Sometimes a rose seedling will turn out to be as ugly as sin, or very sickly, and you will reluctantly have to throw it away. Other times they will be just ho-hum, or look too much like its parent, and therefore have no value. But, just when you don't expect it, you might discover that one of your rose seedlings turns out to be very special.