Well... offering to give comfort can also be considered part of a loving friendship as well. It's not so much that the question was asked, it's your response that could use work.
Like stated above, you could really solve the problem by saying 'If there's anything I can to to help, just let me know' and then happily go about your current activity.
The 'I'm cold' comment can be answered with a 'Would like a blanket?'. Whatever the answer, don't leave the room immediately. Hang around for a few minutes, be happy, then carry on. Remember, it's all part of PMA, and not a show though.
Regardless of how you respond to what's going on around you, she could take the response as P/A - until you show her you really are happy, even when being respectful of her boundaries and feelings.
