So grandma had the right idea in the first place, and she really did know what she was doing. It has always been fun to start roses from cuttings. Some people get their kicks by going "rose rustling" in the deserted cemeteries of old and forgotten mining towns. Others just take a twig from their favorite rose and stick it into the ground in their backyard. There is nothing complicated nor scientific about taking cuttings of roses and rooting them to "start" a new plant. There are various ways of taking rose cuttings, so let's tell you how.
I have successfully taken rose cuttings with both new and old wood. It is important to let the new stems sufficiently mature. The new wood is usually mature enough after the stem has just finished blooming. If you don't let the stem mature enough, then it usually becomes limp and will die before you can get it to root. I take cuttings from new rose stems in the spring right after the first bloom cycle. Then in early to late fall (in Southern California) I prefer to use more mature or old wood. When using old wood in the fall, I will remove the rose cuttings from the Mason jar, baggie, or mister, after only several weeks since it is cool enough then for them to root on their own as long as I water them daily.
One way to stratify the rose seeds is to place the cleaned seeds on a paper towel (a heavyweight brand such as Bounty). Then moisten the paper towel with a solution of half & half purified water and peroxide (to help prevent mold). Fold the paper towel closed, encasing all the rose seeds in the moistened paper towel. Then place the towel full of seeds into a plastic zippered bag. Mark the seed variety and date on the outside of the plastic bag with a permanent marker, and then place the bag into the refrigerator set at about 34-38 degrees. Never freeze the seeds, and do not let them dry out. The moistened paper towel should remain moist in the closed plastic bag for many weeks.
The easiest way to begin experimenting with rose hybridizing, especially for the beginner, is to simply let some of your roses self-pollinate themselves, so they will "go to seed" and set hips. I have found that Playboy, Hurdy Gurdy, Peggy T and Fairhope are some of the easiest roses to set hips, and there are many others. Let the rose hips stay on the rose bushes at least four months before harvesting.
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.