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.
Growing roses from seed can be challenging, since the majority of seeds you collect often won't germinate regardless of your efforts. Fortunately, most rose plants produce a large quantity of seeds inside their rose hips, so it usually isn't necessary to achieve a high success rate. Keep in mind that the plants that grow may be different in appearance or other characteristics from the mother plant, especially if that plant is a hybrid of two varieties grafted together.

Next fill your trays or pots with the potting soil. You can opt to use 50% sterile potting soil and 50% vermiculite, or half peat and half perlite. When the potting mix is ready in the trays or pots, this is the time to take off your seeds from the towel. Remember the seeds must not be removed from the plastic bag until they are ready to be planted. You lightly dust them before planting.
I am curious... it seems that you are just supposed to "soak" the cut stems for a week or more in water.... which is mostly what people normally do with cut roses. But whenever I put roses my boyfriend brings me in water, they just fade within a week or so. I'll "feed" the roses with either sugar in the water or with the packet of plant food that comes with them. I'll cut off a small bit at an angle from the bottom of the stem evert day or so. But after a week or so they start wilting and drooping, so at that point I just take them out and hang them upside down to dry.
Most softwood rose cuttings will root within 10 to 14 days.1 To test their progress, tug very gently on the cuttings. You'll feel a slight resistance as the new roots form and grow into the soil. A gentle fish- or kelp-based fertilizer during this time provides beneficial nutrients. Once roots are established and plants show strong new growth, you can transplant your new roses to more permanent garden homes.
To get the best success, yor rose seed will need a period of stratification (a cold period of about 6-12 weeks). Its a good idea to time this so that it coincides with when they would naturally start to grow in spring – probably around early March, depending on weather conditions. I would look to sowing them in late November/ December and popping them outdoors or if we have a mild winter then stick them in the fridge!
i believe the key to rooting a plant cutting in water is to keep it warm, but not sunburnt in strong full sun. my african violets all seem to root better in water than perlite or soil! the water level is determined by how the mother plant takes water--roses can take lots of water, so root in 3-5" of water. succulents dont like to stand in water, so root in 1/8" of water standing with only the base touching the water.

Cover the cutting loosely, pot and all, with a plastic bag or plastic wrap and keep the soil moist. Putting a tall stake into the pot will hold the plastic away from the leaves. If the plastic touches the leaves, they remain wet and can succumb to a fungus disease. Along the same lines, make sure the condensation can escape from the plastic or the stem will rot.