Cold water being denser would provide better grip for the propeller.

The hull would also be contracted in cold water providing less resistance to water friction.

DeJudge

Brendan, first we must establish a baseline for the statement.

" I have heard that submarines traval faster in cold water"

Are we assuming that the statement is correct. if we agree it is, what evidence do we have in support,

We say that the waterr being colder might improve the grip the propreller has on the water,

The  cold water density is increased reducing the cavitation generated by the propeller, reduced cavitation means less slip.

A modern Sub is shaped like a tear drop, because it provides the most stream lined shape, however any small imperfections in the hull or the trailing edges of protusions such Aerials, diving planes, etc will produce some cavitation.(Noise)

In all the years i have been in the navy i have never seen a painted one, they are usually cast of a bronze alloy, and may polished to a dregree, but any paint applied would wear off  the leading edges fairly quickly, and is not nessersary as the alloy used is corrosion resistant as cast.

If we disagree, we might say the increased water density provides more resistance to forward motion.

Cheers

DeJudge

Following is a simplified answer to the above.

In general cold water is denser than warm water

All other factors being equal, and the propeller revolutions kept constant, a submarine sailing from warm to cold water will experience an increase in both thrust from the propeller and resistance to motion directly proportional to the increase in density.

Initialy the thrust will be greater than the hull resistance,otherwise the submarine is going nowhere, hence the proportional resistance of the thrust will be greater than that of the hull resistance, and the submarine will tend to increase speed, which will be modified  by the fact that the hull resistance is proportional to the square of the speed.

This is a note to Mike Follows of the UK.  In the third paragraph of your response on the Cold Rush question you state that the gas is more soluble in cold water and its saturated vapor pressure is lower and that is why submarines can run silently at higher speeds in cold water.  It sounds like you are referring to oxygen, nitrogen, and carbon dioxide which are relatively low levels compared to the water content.  

I would submit that just the lower vapor pressure of water is involved in the ability to run more quietly in the cold.  The content of dissolved atmosheric gases are even lower in warm waters.   Again the higher water vapor pressure at elevated temperatures would be the bigger contributor to cavitation rather than dissolved atmosperic gases.