Personally, I think your daughter is too small to go to Seoul since it is very cold in Dec. I remembered when my daughter was almost 3, we went to Tokyo in end of Nov, I found it is too cold for her to go and I dare not to go to any "cold" place again with her, so I wait and wait until this year she is going to 7, I will go to Seoul with her in this x'mas.
Don't worry, of sure she will have chance to enjoy a "white x'mas" later.