It's the nature of the gifts of Eru, to his Children. The elves shall not perish while the world exists, but Men may leave the boundaries of it when they die. Where your spirits go, none can say.
I believe that. I would still wed her, but I would not take the journey across the ice if I could change it. I tried to save her, and I couldn't But you're right, my daughter will have the memory of her love for eternity.