As a matter of fact the topic here is qunoot an-Nawazil قنوت النوازل (plural or general term) or qunoot an-Nazilah قنوت النازلة and it is a topic for which both hanbali and shafi'i fiqh is known. Which according a majority is performed after the ruku' in the final witr, it can also be performed at any other prayer in case of necessity. So the practice isn't restricted to Ramadan only nor to al-Witr only.
This is based on the sahih hadith:
Anas b. Malik reported that the Messenger of Allah (ﷺ) observed Qunut for one month Invoking curse upon Ri'l, Dhakwan, 'Usayya. those who disobeyed Allah and His Messenger (ﷺ).
(See ahadith in different length in for example: Sahih al-Bukhari 1, 2, Sahih Muslim 1, 2, 3 and elsewhere like Sunan an-Nasa-i, Sunan abi Dawod and Musnad Ahmad)
As for the report from al-Muwatta' you may find in the commentary of az-Zurqani the following detailled discussion of the Maliki views:
( أنه سمع الأعرج ) عبد الرحمن بن هرمز ( يقول : ما أدركت الناس ) قال الباجي : أي الصحابة .
(He heard al-'A'araj) 'abd ar-Rahman ibn Hurmuz (saying: I never saw the people) al-Baji said: Which means the Companions.
وقال ابن عبد البر : أدرك الأعرج جماعة من الصحابة وكبار التابعين ( إلا وهم يلعنون الكفرة في رمضان ) في قنوت الوتر اقتداء بدعائه - صلى الله عليه وسلم - في القنوت على رعل وذكوان وبني لحيان الذين قتلو�� أصحابه ببئر معونة وفيه إباحة لعن الكفرة كان لهم ذمة أم لا غضبا لله .
Ibn 'abd al-Barr said: Al-'A'araj met a group of the Companions and senior followers (tabi'yn) (in Ramadan, except that they were cursing the disbelievers) in the Witr qunoot, following his dua' - may Allah bless him and grant him peace - in qunoot over Ri'l, Dhakwan and Bani Lihyan who killed his companions at the well of Ma’una. And in it is the permission of cursing the disbelievers, whether they have a covenant or not, out of anger for Allah.
وروى المدنيون وابن وهب عن مالك أن الإمام كان يقنت في النصف الآخر من رمضان يلعن الكفرة ويؤمن من خلفه .
The Medinean students of Malik and ibn Wahb narrated on the authority of Malik that the imam used to perform qunoot in the second half of Ramadan, cursing the disbelievers, and those who were standing behind him said: Amen.
وروى ابن نافع عن مالك أن القنوت في الوتر واسع إن شاء فعل وإن شاء ترك .
Ibn Nafi' narrated on the authority of Malik that qunoot in the Witr prayer is wide, if one wants to do it, and if one wants to leave it.
وروى ابن القاسم عنه ليس عليه العمل ومعناه عندي ليس بسنة لكنه مباح ذكره ابن عبد البر ، لكن روى المصريون أن مالكا قال : لا يقنت في الوتر أي لا في رمضان ولا في غيره وهو المذهب ، وقد قال ابن القاسم : كان مالك بعد ذلك ينكره إنكارا شديدا ولا أرى أن يعمل به .
And ibn al-Qasim narrated on his authority that he does not have to perform it, and its meaning in my understanding is that it is not a sunnah, but it is permissible, as ibn Abd al-Barr mentioned. But the Egyptians narrated that Malik said: He does not recite qunoot in Witr, that is, neither in Ramadan nor at other times, which is the madhhab. Ibn al-Qasim said: After that, Malik used to deny it severely and I'm against doing it.
So basically qunoot at witr isn't a sunnah according the approved view of the Maliki school of fiqh. It is mustahhab to perform it after the second raka'a of sobh (fajr fard) using the known dua' of 'Umar ibn al-Khattab also used by the hanafi school of fiqh at witr prayer (see: Reference of Qunoot Nazila of Umar (RA)).
One may ask why Malik even if he mentioned qunoot in his al-Muwatta' came to the conclusion to not do it. I read that he as one of the students of ibn Shihaab az-Zuhri heard the following hadith:
That he heard the Prophet, after raising his head from the bowing in morning prayer, saying, "O Allah, our Lord! All the praises are for you." And in the last (rak`a) he said, "O Allah! Curse so-and-so and so--and-so." And then Allah revealed:-- 'Not for you (O Muhammad) is the decision, (but for Allah), whether He turns in mercy to them or punish them, for they are indeed wrongdoers.' (3.128)
(Sahih al-Bukhari)
Some people said that Malik heard it via his mate and good friend al-Laith ibn Sa'ad the known scholar from Egypt who was like Malik a student of ibn Shihab az-Zuhri.
Without reading any commentary: This hadith seems to deny the practice of qunoot an-Nawazil.
See also this article -in Arabic- discussing the scholarly views on qunoot an-Nawazil and their evidences on alukha.net.
See also:
Is reciting qunoot mandatory in fajr salat?
What is the source of this dua read in Witr prayer?
What is Dua Qunut and when should we recite it in the Prayer/Salat?
