Why would cold running water be preferred for baptism? The Didache, or Teaching of the Twelve Apostles (an early Christian text not part of the New Testament) says of baptism (chapter 7):


  On the subject of baptism, baptise thus: after having taught all that precedes, baptize in the name of the Father and of the Son and of the Holy Spirit, in living water. If for some reason you do not have living water, baptize in other water; and if you are not able to in cold water, in warm water. If you do not have enough of one or the other, pour out water three times on the head, in the name of the Father and of the Son and of the Holy Spirit. Before the baptism, let the baptizer, the baptized and others who can, observe first a fast; as for the baptized, you must enforce a fast beforehand for one or two days.


"Living water" is usually assumed to mean "running water", like the river Jordan in which Jesus was baptized.

What is the reason for preferring running water over still water, and cold water over warm water?

I know some people who were baptized in the sea; would that count as living water, or does the term only refer to rivers? (It certainly met the preference for cold water, by all accounts.)
You may find this link of interest:

http://www.theropps.com/papers/Winter1998/regeneration.htm

And here is the significant part, where they talk about the significance of running water and cold water:


  The main points here related to the topic of regeneration are (as in
  Ignatius' works) implicit, in a discussion primarily centered around
  the baptismal mode. There is a stress on baptism in living and cold
  water. Living water is likely preferred because rivers had symbolic
  significance as boundaries of transition in the ancient world. The
  living water emphasis also has Jewish parallels. Water which was
  running is also still connected to its natural source (J. Draper. The
  Didache in Modern Research. Leiden: E.J. Brill. 1996:46,218). Cold
  water may have been prescribed because of the shocking nature, which
  would make baptism a memorable event. Interestingly, however, if these
  types of water are not available, or even if enough water is not
  available to immerse, the great importance of baptism is seen in the
  admonition to do so in at least some fashion regardless of the
  resources at hand. The emphasis of living water is especially
  consistent with concepts of a change in the baptized person's life.


I found this quote of interest, if you search for the word 'leper', in http://www.christian-history.org/water-baptism-quotes.html, as it would seem that running water would also be better if we are to be cleansed.


  For as we are lepers in sin, we are made clean by means of the sacred
  water and the invocation of the Lord from our old transgressions,
  being spiritually regenerated as new-born babes,


There are other thoughts that this is based also on the Jewish traditions, but I think that is getting into a different area than the question was intended.