You are right , there are many opinions about the subject.
1.- It does not make any damage to cool the die, the cost involved to send water in and out of the die could be the only inconvenient, the volume of water required per die is small.
2.- To keep the die cool is supposed to help to keep the plasticity of the lubricants( calcium and sodium stereates)which makes the lubrication more effective.
3.- The die life is also increased if the heat generated in the die is dissipated.
4- Removing the heat from the die , also helps to diminish the heat generated in the wire.
The above factor are directly proportional to the drawing speed , and tensile strength of the material being drawn.
Eduardo Anaya
Senior Consultant
INDEPA S.C.
Mexico City
Tel(011-52)555-407-7451
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