Growing roses from seeds is not the fastest method for propagating roses but has several advantages. Roses from seeds take a little longer but then you end up developing a new set of varieties. Professional hybridisers select a new line of easy to grow and disease resistant rose to propagate. However, for you, each seedling will be a surprise when they finally bloom. It is like opening your birthday present when you were a kid. You never really knew what to expect! That is the same feeling seeing those little seedlings opens up for the first time.
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.
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.