Did Martin Luther effectively teach that our justification is like white snow covering over dung? 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 described God's forgiveness as Christ simply covering
  over our sinful souls, like a blanket of snow covering a manure heap. - cf. @Verbum's post in On Jesus' blood covering sins | Catholic Answers Forums and 2nd to last paragraph here.


Is there a reference that would show that Martin Luther did in fact state or teach this? If he didn't say this, what did he actually say that may have led to this re-stating?

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, God looking down sees only the white snow but not the dung underneath that still remains)?

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



Please see also Christians are doomed to hell? | C.SE. It turned out that what has been claimed that a community taught, has actually never been an official teaching of that community.
According to this article: Has Martin Luther's "Snow-Covered Dunghill" Mystery-Legend Been Solved?! the answer to the question is, "No, he did not say that, but it sounds like something he would have said."

Luther said:


  Conceived in sorrow and corruption, the child sins in his mother’s
  womb. As he grows older, the innate element of corruption develops.
  Man has said to sin: ‘Thou art my father’—and every act he performs is
  an offense against God; and to the worms: ‘You are my brothers’—and he
  crawls like them in mire and corruption. He is a bad tree and cannot
  produce good fruit; a dunghill, and can only exhale foul odors. He is
  so thoroughly corrupted that it is absolutely impossible for him to
  produce good actions. Sin is his nature; he cannot help committing it.
  Man may do his best to be good, still his every action is unavoidably
  bad; he commits a sin as often as he draws his breath. (Werke, (Wittenberg Edition), Vol. III, p. 518.)


In Luther's commentary on Psalm 51:7, which refers to snow cleansing our sins:


  "How can we become "purer than snow" even though the remnants of sin
  always cling to us? I answer: I have always said that man is divided
  into spirit and flesh. Therefore, as far as the total man is
  concerned, there remains remnants of sin or, as Paul calls them (2
  Cor. 7:1), "defilements of body and spirit." . . . Still we have
  obtained Baptism, which is most pure; we have obtained the Word, which
  is most pure; and in the Word and Baptism we have by faith obtained
  the blood of Christ, which is surely most pure. According to this
  purity, which in spirit and faith we have from Christ and from the
  Sacraments that He instituted, the Christian is rightly said to be
  purer than snow . . . even though the defilements of spirit and flesh
  cling to him. These are concealed and covered by the cleanness and
  purity of Christ . . . 
  
  . . . if you look at a Christian without the righteousness and purity
  of Christ, as he is in himself, even though he be most holy, you will
  find not only no cleanness, but what I might call diabolical
  blackness. . . . Therefore if they ask: "Sin always clings to man;
  how, then, can he be washed so as to make him whiter than snow?" you
  reply: "We should look at a man, not as he is in himself, but as he is
  in Christ."


The linked article above provides many more words from Luther, and goes much deeper into detail about the question, and even quotes a "snow over refuse" analogy by Luther, but that analogy has more to do with his belief in sanctification. The conclusion in the article is that Luther did not exactly describe God's forgiveness as Christ simply covering over our sinful souls, like a blanket of snow covering a manure heap, but that this unofficial quote was constructed from many different things that Luther did say.