Good question. It's well known that cold induces cutaneous vasoconstriction, but it's only been fairly recently that molecular investigations have begun to look further. It's likely that Rho activity and Rho-kinase play a role. Here are a couple papers with data in vivo and in vitro:

http://www.ncbi.nlm.nih.gov/pubmed/17172270

http://www.ncbi.nlm.nih.gov/pubmed/15087420

Also, I'm not certain that there is specifically a reduction in inflammatory response with cold therapy through the usual inflammatory mediators. Inflammation still occurs, but the cold is reducing blood flow to the area and thus non-specifically reducing overall cell transport to the region. Fewer leukocytes in the region would then dampen the inflammation.

Best,

DB