Over the internet I have come across posts like this that say

Luther stated that our sinful state is much like the piles of manure. It is ugly, repulsive and offensive. There is nothing in it that would commend it to anyone, especially God – but justification is like the first snowfall in winter. It covers the sight and smell of the manure piles with a blanket of pure white. The pile is still inherently a manure pile, but now it is covered.

And others variants of it e.g.

Martin Luther's described God's forgiveness as Christ simply covering over our sinful souls, like a blanket of snow covering a manure heap.

Is there a reference that would show that Martin Luther did in fact state or teach this?

If he did teach this, how does Lutheranism or those understanding or agreeing with this perspective reconcile this teaching with Scripture that God in his Christ does actually take way the sins of the world¹ and not just cover them over - i.e. when we have been justified by Christ, Good looks down only sees the white snow but not the dung underneath that still remains?

^{1. John 1:29 (RSVCE), Heb 9:22-24 (RSVCE), etc.}