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. 

I bought hybrid tea roses last year. Not long after the first blooms, we moved one because it was interfering with the sprinkler system. It looked unhappy at first, but continued to bloom throughout the season. This year, it does not have so much as one leaf, no new foliage whatsoever, however, there is still green inside the stem towards the base of the cane. Is it done for, or is there a chance it will come back in it's second rear?
Prune the roses. Pruning roses keeps them both beautiful and healthy. The goal is to clear away crowded areas to open up the bush, which helps prevent rotting and disease. The pruning strategy differs according to the season, but the cut you make is always the same: prune just above a bud eyes, the areas where branches form. They look like small circular swells and are usually located above a set of mature leaves. Make a down-slanted cut on an outward-facing bud eye.
Pruning: Dead, weak and sickly stems can lead to disease problems. Pruning these away will increase air circulation to the center of the plant and minimize fungus problems. Pruning also stimulates new growth, and allows you to shape the plant in a pleasing manner. Spent flowers should be removed during the growing season to encourage reblooming. Use a scissor-action pruner for the cleanest cuts.
Remove the seeds from the fridge. Try to do this around the time that the seeds would normally start to germinate, such as in early spring. Make sure that the environment outside of the fridge is about 70 degrees Fahrenheit.[3] The seed will not sprout until you take them out of the fridge. Depending on the rose variety and individual seeds, the seeds could take anywhere from four to sixteen weeks to germinate. Often, 70% or more of the seeds never sprout at all.[4]
Northern gardeners need to know exactly what zone a rose is hardy to. Southern gardeners must also watch to see what zones are recommended for each particular variety, as some roses perform very poorly in hot and/or humid weather. Read the catalogs carefully and, if possible, purchase your roses from a local or regional grower. They will be able to advise you from experience about how a particular variety will perform in your area.
Plant the rose bush seeds approximately ¼ inch deep in a seed-planting mix in seedling trays or your own planting trays. The trays need not be more than 3 to 4 inches deep for this use. When planting rose seeds from various rose bush hips, I use a separate tray for each different group of seeds and label the trays with that rose bushes name and planting date.
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.   
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