Ibn Qudaamah in his Al-Kaafi fi fiqh Al-Imaam Ahmad states regarding Qunut in Witr, “And when the Imam performs Qunut, the one behind him says Aameen. If he does not hear the Qunut of the Imaam, then he is to make du’aa, and there is textual proof (nass) for that. And [one] raises his hands in the Qunut to the level of his chest, due to Ibn Mas’ood doing so. When he has completed his du’aa he wipes his face with his hands. It is also reported from it [i.e. the madh-hab] that it is not done. And the first [opinion] is better due to what is reported from As-Saa’ib ibn Yazeed (from his father) that Rasulullah (SAWS) (sallallahu ‘alayhi wa sallam) would raise his hands when making du’aa, and wipe his face thereafter with his hands. Reported by Abu Daawud.”
The matter is that Hanafis also raise their hands due the report of Ibn Mas'ood, but they raise it for the takbir of Qunut like when raising the hands when opening the salah, thus not DURING the dua of Qunut.
The Hanbalia have interpretated the action of Ibn Mas'ood in a different manner? Or what are the proofs of the Hanafis and Hanbalis?
Was salaam

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.

The evidence provided by the Hanbali School of jurisprudence about the permissibility of raising the hands when supplicating in Qunoot is the general evidence which proves the permissibility of raising the hands when supplicating and also the specific evidence about raising the hands in Qunoot.

For example, among the general evidence is what Ibn ‘Abdur-Rahmaan ibn Qaasim An-Najdi stated in his book entitled ‘Haashiyat Ar-Rawdh’ as he said: “Maalik ibn Yasaar narrated: “the Prophet said: “Supplicate Allaah with the palms of your hands and do not supplicate Him with their backs upward).” [Abu Daawood]

Moreover, the Prophet said: "Your Lord is bashful (which implies not refusing or rejecting one's supplication) to turn away His Slave empty-handed (i.e. not responded to) when he raises them to Him asking Him for any good." [Ahmad, Abu Daawood, At-Tirmithi and Ibn Maajah] Besides, one should leave space between his hands (when raising them up). Moreover, raising the hands when supplicating is confirmed with Tawaatur (i.e. transmitted by a group of narrators from a group of narrators, generation after generation and so forth, and they are all trustworthy people and it is absolutely impossible for them to agree on a lie).

On the other hand, among the specific evidence that is reported about raising the hands in Qunoot, is that it is reported that ‘Ibn Mas’ood raised his hands in Qunoot to his chest; it is reported that ‘Umar and Ibn ‘Abbaas, used to do so as well, and this is the view of Is-haaq (Ibn Raahawayh), ….because the companions whom we mentioned did so." [as stated in Al-Mughni by Ibn Qudaamah]

As according to the Hanafi School of jurisprudence, it is legislated to raise the hands at the beginning of Qunoot –like raising them for starting the prayer –and then to put them down. However, they have not provided any evidence or justification for this. It should be mentioned that according to the other opinion of the Hanafi School of jurisprudence is to raise the hands and keep them raised when supplicating for the Qunoot, as stated in “Haashiyatu Ibn ‘Aabideen” which reads. It is also said that it is like when one supplicates –as it is narrated from Abu Yoosuf that one should raise them to up to the level of his chest while turning their palms to the sky. It appears according to this narration, that he keeps them in this position (i.e. hands raised up) until the end of the supplication.”

Allaah Knows best.