Rose seeds need to go through stratification (an artificial cold spell) for 10 to 12 weeks before they will sprout. This, combined with a germination success rate of 20-30% makes propagation by seed an unattractive prospect. on by seed an unattractive prospect. If you still want to try it, find a good source of information that will guide you through the process.
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.
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.
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.