The coldness of Edward’s skin was always very noticeable to Bella.  The first time they accidentally brushed fingers, she pulled away as if she had been burned.  Edward did the same because he didn’t want her to discover the truth about him.  When they embraced, Bella could feel the cold right through her clothes.  But she didn’t find this unpleasant at all.  Bella described how good Edward’s cool lips felt against hers when they kissed.  After Bella becomes a vampire, she is now one of The Cold Ones.  When she first touches Edward after she is changed, Bella is surprised to find Edward’s skin no longer feels cold to her, but pleasantly warm.