I have previously heard that, if there are multiple simultaneous painful stimuli, the mind will only feel the sensation of pain from the most severe injury. A large amount of googling has turned up nothing and PubMed searches are proving tricky as I cant find the name of this effect (if it exists).

If it does exist, is the mechanism solely effective for pain signals or would we for example only feel cold at our coldest points (i.e. from the face or the hands rather than both) on a frosty morning?

I cannot help you locate any research but have two related observations:

 

1. I think it is more a matter of focus. One can still be aware of multiple pain sources, but is most conscious of the worst.

2. I can assure you that going out into a Scottish winter morning improperly dressed produces the sensation of cold in all parts of the exposed anatomy.