Technically, these fluids being oil-based fluids, cannot freeze. However, certain conditions like extreme cold can lead the fluid to become thick. It can further prevent the fluid from transferring from the master cylinder to the wheels. Overall, it has a working point temperature below, which makes the pedal stiff, thereby hampering the braking system but not a failure. If your brake fails, it cannot be because of the thickness of the fluid. There might be other causes like condensation in the brake booster or frozen vacuum supply hose.