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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.