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.
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.
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.

Please keep in mind that many rose bushes are grafted rose bushes. This means that the bottom part is a hardier rootstock that will withstand cold and heat better than the top and more desired part of the rose bush. Starting a rose bush from cuttings places the new rose bush on its own roots, so it may not be as hardy in cold climates or in extreme heat conditions climates. Being on its own root system can cause the new rose bush to be far less hardy than its mother rose bush.
Growing roses from seed is certainly not the fastest method of propagating roses, but I can assure you it really is the most rewarding. However, rose hybridizing is surely a lesson in patience, since your success rate can be very small, and it may take several years to reap your rewards. Imagine opening up presents on your birthday or at Christmastime when you were a kid. Well, that's how it feels to see those little rose seedlings open up for the very first time. You never know what you will find inside.   
Select two roses that you want to cross-pollenate. The blooms should not be too tight, perhaps about one-half to 3/4 open. Carefully peel off all the petals. The rose stamens inside should look golden yellow and fresh. With sterile tweezers or cuticle scissors, carefully remove all the stamens at the base of the rose hip, so you do not damage the pollen sacs (anthers). Place the rose stamens into separate, clean film canisters, and place the canisters in a dry place, but not in direct sunlight.   
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.
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