Interesting theory, I honestly think Jon is dead but I wanted to highlight this part. In ASOS, Sansa feels wetness from snowflakes in her face, do you think this could be foreshadowing to Sansa dying (during the war for the dawn)? The mention of the statue of the weeping woman and Sansa falling to her knees adds to this.
Drifting snowflakes brushed her face as light as lover’s kisses, and melted on her cheeks. At the center of the garden, beside the statue of the weeping woman that lay broken and half-buried on the ground, she turned her face up to the sky and closed her eyes. She could feel the snow on her lashes, taste it on her lips. It was the taste of Winterfell. The taste of innocence. The taste of dreams. When Sansa opened her eyes again, she was on her knees. She did not remember falling. It seemed to her that the sky was a lighter shade of grey. Dawn, she thought.
In the same chapter:
Robb had melting flakes in his hair when he hugged me.
And GOT Jon IX:
He remembered Robb as he had last seen him, standing in the yard with snow melting in his auburn hair.