I guess the easy answer would be that 'the snow queen' refers to the story as a whole and not just the particular character. But I guess it goes further than that as I think my fundamental issues flow from someone who I do identify as the 'snow queen' and who thus sets off the entire Gerda-Kay complex? Someone with a narcissistic personality...

Perhaps most importantly, I actually identify more with Kay than with Gerda. It is Kay who gets the splinter of glass/ice in his eye and in his heart. It is Kay who is seduced by the Snow Queen's finery and finally it is Kay who ends up numb and paralyzed in an ice palace, trying to complete an impossible puzzle. I think Gerda is a hard act to follow! She is plucky, resourceful, and devoted. Plants, animals and other people are attracted to her and come to her aid. Even supernatural agents are on her side! Perhaps there is an element of Gerda in me - a part that is compassionate and devoted. However, the compassion is not for Kay and neither is the devotion because most of the time Kay just doesn't seem worth it...

Sometimes I manage to drum up a feeling of 'unconditional love' for Kay-part, but it's far easier for me to loathe it. Which I guess is an internalized Snow queen?