I don't know what that means. If I had to guess I would guess that you have either galvanized pipe or polyethylene (black plastic).
Rust from inside the galvanized would appear brown, not black.
The polyethylene may or may not burst from freezing. I don't think it would disintegrate from freezing.
That leaves the pump and the tank as possible sources of the black specks.
It could only be the pump if it has a plastic impeller. Unless the pump is a very cheap one I would not expect the impeller to be plastic but I suppose it could be.
Inside the tank is a rubber bladder, sort of like a balloon. Again I would not expect it to disintegrate from freezing.
To isolate the source of the black particles,
First, make a note of the pressure that the pump comes on and the pressure that it turns off.
The tank should have a drain valve on it or on the piping between the pump and the tank.
Turn the breakers to the pump off. Attach a hose to the drain valve and drain the tank into a bucket. Look for black particles. If there are black particles you will know that they came from the tank, the pump or the well. If no black particles start looking at the piping to the house for the source.
If you find the black in the bucket, turn the breakers to the pump back on. Leave the drain open and again pump water into the bucket. If you find black it is coming from the pump or the well.
If you don't find black after pumping directly from the well, it is probably coming from the tank.
Turn pump breakers off. On the tank you will find a valve stem, just like on a car tire. Using a tire pressure gauge see what air pressure is in the tank. The gauge should read two pounds less than the pressure at which the pump comes on.
If the gauge reads zero you have a ruptured bladder in the tank. The black particles may be from the bladder.