An assumption regarding how Macbeth would react should be based on Macbeth's train of thought at the time he wrote his letter and how he responded upon reuniting with his wife.
When Macbeth and Banquo meet the witches, they greet him with the title 'Thane of Cawdor' and predict that he shall be king. Macbeth is greatly affected by the prediction, so much so that Banquo notices his reaction. Later, Angus informs Macbeth that King Duncan had bestowed the title 'Thane of Cawdor' upon him. Macbeth then comments in an aside:
'Glamis, and thane of Cawdor!
The greatest is behind.'
This clearly expresses Macbeth's ambition. One of the greatest hurdles in his desire to become king has now been breached. The fact that he, at this point, possesses two titles brings him closer to the throne. Macbeth, in a later aside, also expresses his intention that come what may, he should press forward in achieving his goal.
Lady Macbeth receives her husband's letter which informs her of the witches' predictions and that one had actually come true. She is thrilled but fears that her husband is 'too full of the milk of human kindness to catch the nearest way'. She expresses doubt that Macbeth is remorseless enough to murder Duncan. She wishes that Macbeth arrives soon so that she may encourage and inspire him to achieve that which 'fate and metaphysical aid' have guaranteed him - the crown of Scotland.
Macbeth would obviously be proud of his wife for supporting him in his ambition and would love her ever the more for it. He might, however, feel somewhat offended that his wife believes that he is not ruthless enough to go through with the deed. After all, he is a brave soldier who has faced many enemies and has never backed down from any challenge. Was it not he, for example, who 'unseamed' 'merciless MacDonwald' 'from the nave to the chaps'?
In their conversation later, Macbeth does express doubt, but Lady Macbeth convinces her husband to go through with the deed, with her providing him the necessary support. Thus the scene is set for Duncan's ignominious assassination.