I saw a similar question asking why a shower gets hot/cold when toilet is flushed. My question is why does the person in the shower get cold If anyone anywhere in the house turns on the water? I cannot do dishes, run the washer or flush the toilet without someone getting froze out in the shower! Very frustrating!
If flushing the toilet results in COLD water coming out of the shower it sounds like a pressure issue.
Typically flushing the toilet (which reduces the amount of cold water pressure in the line), would cause the shower to become too hot.
However, if the pressure in your system comes prior to where the cold feeds the hot water tank, then flushing the toilet could cause a pressure reduction in the hot line causing the hot line to diminish.
Solution would presumably be a pressure tank addition to the feed to the water heater before the tank but after the junction with the cold water, and a check valve to ensure the tank can only pressurize in one direction.
Suggest strongly you consult a plumber on this.