Well, after a hot shower, my skin is very soft and relaxed and my pores are open. After a cold shower, my skin is tighter and more closed up. For a simple barometer of the difference, observe the difference between your own nipples after a hot soak vs. after a cold bath.
We also know that hot water vs. cold water affects non-living things differently. From washing clothes to doing dishes. Hot water makes things dissolve in it more quickly and effectively. Water is a better solvent when warm or hot than cold.
My course of action is to use warm water on my skin to open the pores, soften the skin, and soften the hair for shaving. Then, after shaving, I use cold water to close my pores and tighten my skin. But it might even be best to use warm water after a shave also, to allow your after-shave and/or moisturizer to soak into your skin better.