Drain pipes that take out the toilet's waste and used water are totally separate from the supply pipes, one of which brings water into the toilet. If the supply pipes are frozen, you can likely only flush the toilet one time, unless you manually add water yourself. If the drain pipes are blocked because of a freeze, you can't flush the toilet.
Frozen Supply Line
If the supply line is frozen, you can flush the toilet once and use the water already stored inside the tank. The frozen pipe prevents fresh water from flowing into the tank to refill it, and the bowl's water level will also be low, because some of the tank water is diverted down to completely fill the bowl. If the pipes remain frozen and you need to use the toilet, get buckets of water from another source, such as a sink where pipes are not frozen. Pour cold water into the toilet tank, or pour the water directly into the bowl to flush the toilet after using it.
Frozen Drain Pipes
The drain pipes are less likely to freeze, but if it does happen, don't flush the toilet or it will just back up into the bowl. Eventually, water will spill over onto the floor if you keep flushing it before the water has a clear path to exit through the plumbing. One possible solution to clearing out ice in the toilet's drain pipe is to pour a bucket of hot water down the toilet drain.
An additional consequence that sometimes arises after cold weather blows through and pipes freeze, is that a vent stack or main line gets clogged. Afterwards, the toilet backs up and you can't flush it. In this instance, another fixture's drain -- such as the bathtub -- will also back up with water. To fix this and so you can flush the toilet again, insert the cable of an auger down through the vent pipe on the roof, to reach and break up the blockage. To clear out a main line, insert the auger cable through a cleanout.
Thawing the Pipes
In addition to pouring hot water down the drain to help unfreeze a toilet's drain pipe, use other methods to thaw out frozen pipes. If not, waiting for the pipes to thaw out on their own sometimes takes several days. Open the sink faucets near the toilet, and begin thawing the pipes as close to the open faucet as possible. For pipes inside the house, open cabinet doors that hide pipes and turn the inside heat up. If a pipe is already slightly thawed, wrap it in rags and continuously pour hot water on it. Or, move a portable electric hair dryer back and forth across sections of frozen pipe to thaw them.