"really"....an adverb, would be used to modify a verb, an adverb or an adjective.  Had I said "cold weather", cold would have been an adjective and, thus, required the adverbial modifier.  However, I said cold...which is a "state" and, therefore, is a noun, thusly, requiring an adjective and therefore the term REAL....  

  cold noun
BrE /kəʊld/ 
; NAmE /koʊld/ 
 
Add to my wordlist
low temperature
 [uncountable] a lack of heat or warmth; a low temperature, especially in the atmosphere He shivered with cold. Don't stand outside in the cold. She doesn't seem to feel the cold. You'll catch your death of cold (= used to warn somebody they could become ill if they do not keep warm in cold weather)"

be happy to play grammar pedantics with you sometime.  It's really rather fun,  or should I say it's real fun.  regards, Gary