Sometimes the matter of whether the dough should be allowed to "proof", or rise, before or after cold fermentation is a philosophical one. For example, Tom Lehmann, of the American Institute of Baking and an acknowledged expert on pizza doughs, prefers to cold ferment pretty much all pizza doughs and shape them later, after the cold fermentation. An example of a dough recipe that Tom has recommended for pan pizzas and where the shaping is done after cold fermentation is at the PMQ Think Tank at http://thinktank.pmq.com/viewtopic.php?p=37687#37687
Usually, when one wants to achieve above average volume in a pizza crust, the dough is allowed to "proof", or rise, before baking. This is common for Sicilian, pan style and Greek/pan pizzas, and focaccia as well. It can actually be used for almost any style, including NY and a Papa John's American style pizza, although most people do not use a proof approach for those styles. Those doughs are tempered for a brief period but, unliike the other styles mentioned above, they are not proofed in order to get added height in the finished crust.
Whether a dough is to be subjected to a single or multiple fermentations is usually dictated by the dough recipe used. For example, Neapolitan style doughs often go through a bulk rise and individual rises after division. Emergency doughs intended to be made and used within a few hours also often go through two fermentation periods. I have seen a few dough recipes where dough balls are punched down one or more times during fermentation, both at room temperature and in the refrigerator, but those are not the most common methods. Absent a recipe and instructions to guide you as to when to use multiple fermentation periods, it will usually be as a result of a lot of experience and experimentation with doughs to tell you when you should use a single or multiple fermentations. There are no simple rules and often the course to take is not particularly intuitive.
You can read some other thoughts that I have had on this general subject at Reply 7 at http://www.pizzamaking.com/forum/index.php/topic,3798.msg31749.html#msg31749
. You might also read the other posts in that thread.
I agree with Randy that one should follow the instructions given for a particular dough recipe. All too often, people freelance and when they get poor results they end up blaming the recipe rather than their deviations.