Reynaud's syndrome means that a person has an extreme, and harmful, form of the normal reaction whereby the body withdraws blood from the extremeties in order to help keep the vital organs warm. This is a natural function and essentially means that the body treats the extremeties as expendible when it gets too cold and will sacrifice them in favour of organs like the heart, lungs, liver and brain. Warm blood is withdrawn to prevent it cooling down and kept nearer the centre instead. This is why your core temperature is much more important than the condition of your hands. If your core temperature drops then this is hypothermia which can quickly kill.
People with Reynaud's have an extreme over-reaction to even small drops in temperature, their bodies react as though exposed to severe and prolonged cold and withdraw blood supply from the hands and feet.
This is why a Reynaud's attack shows as fingers which instantly turn a blue-white colour and become very cold as the blood supply in withdrawn. The main danger is that if this is prolonged then the tissues can become starved and start to die, they can then turn gangrenous - in exactly the same way that frostbite works.
As said, withdrawal of blood can also be a response to emotion - anger or fear cause the body to go into "fight or flight mode" as adrenalin floods out to prepare the body to flee or do battle at maximum efficiency. To hep, blood is withdrawn to the vital organs so that the heart can pump faster and stronger, breathing increases to provide extra oxygen, to give extra power to the muscles.
This is why episodes of Reynaud's can also be triggered by emotional states.
When someone becomes very angry or frightened they tend to feel cold and clammy, espescially afterwords. The body ignores and over-rides these feelings temporarily as they are a distraction in a situation of potential danger.
I would suspect that it is the aggressive or fearful moods that is triggering "flight or fight" and that your mum is having an exagerrated response, leaving her hands icy cold.
It would be a good idea to have this checked by a doctor, since it could be Reynauld's, or indicate a problem with circulation.