Does original sin have an impact on Jesus? Was Jesus subject to original sin or because he was born of the Holy Spirit and of Mary he was not born with a sin nature?
Does original sin have an impact on Jesus?

Like any coin worth it weight in gold, this question has two sides of an equation, just like a coin of great value.

The question is both yes and no!

Let me try to explain this.

On one side of the coin, Jesus was conceived without original sin and as such was spared from all stain of sin inherited from Adam’s disobedience.

It is true that some denominations believe that Mary was conceived without original sin by a unique privilege bestowed onto her by Almighty God. Catholics call this the Immaculate Conception of the Blessed Virgin Mary.

Furthermore, St. Thomas Aquinas maintains that it was indeed possible for Our Lord Jesus Christ to have been born of sinful woman; Christ's glory would not have been diminished thereby. But, he states elsewhere, it would have been inappropriate:


  God so prepares and endows those, whom He chooses for some particular office, that they are rendered capable of fulfilling it, according to 2 Cor. 3:6: "(Who) hath made us fit ministers of the New Testament." Now the Blessed Virgin was chosen by God to be His Mother. Therefore there can be no doubt that God, by His grace, made her worthy of that office. ... But she would not have been worthy to be the Mother of God, if she had ever sinned. First, because the honor of the parents reflects on the child, according to Prov. 17:6: "The glory of children are their fathers": and consequently, on the other hand, the Mother's shame would have reflected on her Son. Secondly, because of the singular affinity between her and Christ, who took flesh from her: and it is written (2 Cor. 6:15): "What concord hath Christ with Belial?" Thirdly, because of the singular manner in which the Son of God, who is the "Divine Wisdom" (1 Cor. 1:24) dwelt in her, not only in her soul but in her womb. And it is written (Wis. 1:4): "Wisdom will not enter into a malicious soul, nor dwell in a body subject to sins."
  
  We must therefore confess simply that the Blessed Virgin committed no actual sin, neither mortal nor venial; so that what is written (Cant 4:7) is fulfilled: "Thou art all fair, O my love, and there is not a spot in thee," etc. - Was the dogma of the Immaculate Conception formulated in response to someone challenging Mary's ability to bear a perfect Son?


Also according to St. Thomas Aquinas only Adam was responsible for transmitting original sin to the human race and thus it follows that only the Holy Spirit was responsible for preserving Christ from original sin, not Mary.

St. Thomas Aquinas in his Summa clearly states that it was Adam and not Eve that was responsible for the transition of original sin. Now if Mary, the Mother of Jesus is the New Eve and Jesus Christ is the New Adam, it is obvious that the Immaculate Conception was not necessary for our salvation for the Holy Spirit can operate in that dwelling place He so chooses to. It the Holy Spirit that made it possible for Christ to be free of original sin and not Mary, the New Eve.


  The solution of this question is made clear by what has been said. For it has been stated that original sin is transmitted by the first parent in so far as he is the mover in the begetting of his children: wherefore it has been said that if anyone were begotten materially only, of human flesh, they would not contract original sin. Now it is evident that in the opinion of philosophers, the active principle of generation is from the father, while the mother provides the matter. Therefore original sin, is contracted, not from the mother, but from the father: so that, accordingly, if Eve, and not Adam, had sinned, their children would not contract original sin: whereas, if Adam, and not Eve, had sinned, they would contract it. - Whether if Eve, and not Adam, had sinned, their children would have contracted original sin?


Just as St. Paul states, Jesus is without sin.


  For we have not an high priest which cannot be touched with the feeling of our infirmities; but was in all points tempted like as we are, yet without sin. (KJV) - Hebrews 4:15


Now on the other side of the coin, all mankind was stained with both original sin and actual sin and this did have an impact Jesus because he died saving sinful mankind from their sins.

Jesus Our High Priest was born in order to save man from their sins. Jesus suffered his Passion and Death for our salvation.  Only in this sense did original sin have any impact on Jesus who is called the Christ.

Although he himself had never been stained with original sin; he did suffer his Passion and Death for mankind who truly did suffer for original and actual sin.