The plant will become dormant—and you want it to stay that way; it is the natural state. After the first deep freeze, put is in a room or place (garage) with no heat and natural light (window). You can add some water occasionally but this is not intended to be “watering”; the plant is dormant and will not take it up but the soil can be lightly moist. Bring the plant back outside when it shows signs of coming back to life. Plant it, per the guidance above, when the soil warms.
As soon as the rose seeds have been removed from the rose hips, rinse the seeds in a solution of purified water (any bottled water will do) with 5% bleach. This would be about two teaspoons of bleach per cup of water. Rinse the rose seeds with plain bottled water in a strainer, then soak the seeds in straight 3% peroxide for 24 hours. CAUTION: Do not mix bleach with peroxide because there could be a chemical reaction.
When the rose hips are ripe, after about four months, cut them off the bush. Some rose hips will turn yellow, orange, or red, but others stay green even when they are ripe. You can open the hips as soon as harvested or you can store the unopened hips in the refrigerator for several weeks before opening. Then slice the rose hips in half, and open them with a knife. A butter knife will do just fine. Now, dig the rose seeds out of the rose hip with the knife, and throw away the pulp and outer shell.
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. 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.
The rose seeds can be planted right away if you have harvested them as late as November, December or January (in Southern California) or early spring after danger of frosts in your area. Place the rose seeds about one-half inch deep in a very light mixture of 50% sterile potting soil and 50% vermiculite. Some rose hybridizers use Sunshine Mix #4. You can use small pots or shallow trays to plant your seeds, whatever works for the space you have, as long as they have good drainage. Nursery flats work well for this. Lightly dust the rose seeds with RooTone or Captan before covering with soil. And then dust the top of the soil again, which will hopefully help to prevent damp-off (a disease which kills young rose seedlings). Amateur rose hybridizers concerned with toxic chemicals may want to periodically spray the seed tray with diluted peroxide and water instead of the more toxic Captan.
After the rose seeds have soaked overnight, rinse them in a strainer and place them into the blender with at least a cup of plain purified water (making sure all seeds are covered), and turn it on for a few minutes. It usually doesn't chop up the seeds, but rather, it will clean off the pulp remaining from the rose hip, which would otherwise mold if left on the rose seed. You may see a few seeds chopped up, but those usually aren't viable anyway. Flush the rose seeds again through a strainer using fresh purified water.