It depends on the weed. Normally if it is an annual it will be killed. However if not annual it may go dormant, grow stronger roots, or continue growing all winter. This is the same as any plant in your garden.

Some weeds are fall annuals, the same as winter wheat. They will germinate and become established in the fall, generally taking advantage of a time of year when temperatures are cooler, competition from other plants is low because they are dying or going dormant for winter, and showers tend to provide soil moisture. Usually they don't get very big in the fall and you may not notice them. Then the next spring, when the frost goes out of the ground, they have an established root system and take off, getting a leap on the spring weeds, using the moisture that accumulated in the soil over the winter, and produce seed before the heat of summer. Many mustards will behave this way, as will cheatgrass.

If you cultivate the ground before it freezes for the winter or early in the spring, they are easy to control because they are still so small and any disturbance will usually eliminate them. Herbicides will generally be very effective in the fall, also. However, herbicides have a much tougher time in the spring after the plants start to send up flower stalks or seed heads.

beeone , how do I cultivate the ground?

All you need to do is move the top 1/4-1/2" of soil. The weeds have a very delicate root system when they get started in the fall, so if you can stir that top 1/2", you will either uproot them to dry out or cut the roots off from anything deeper so they dry out with very little effort.

If you are dealing with a lawn, then you have a problem because you can't stir the soil. Otherwise, use a hoe or garden cultivator or rototiller. The key is to move the soil a little so as to disrupt the roots. A rototiller would go deeper, but that isn't a problem when it isn't your muscle going deeper. With a hoe, you are just scratching/scraping the surface, which is much easier than chopping down into the soil.

An annual will die whether it gets frosted or not, that is just the nature of those plants, grow, produce seed, and die in one year. If the "weeds" you wish to control are in a garden the simplest, easiest method of control is to cover them up and deny them access to the sunlight that all plants need to grow and those "weeds" will die and put back into your soil the nutrients they took out.
If the "weeds" are growing in your lawn getting rid of them might be a bit more difficult, but properly feeding that lawn, maintaining a good, healthy soil for that lawn to grow in, mowing the grass high, and proper watering will do as much to control "weeds" and spraying will.
There is also a school of thought emerging that says a lawn does not need to be "Weed" free and you are not a bad, evil person, to be shunnned, if your lawn does have a few "weeds" in it.