Based on FAO, I will use the name Corkscrew Walachian / Valachian, altho Wikipedia has it as Wallachian Sheep.
Both quotes below are from Pastoralism And The Romanians History - People, Languages, Genes And The Local Sheep Breeds, In North-Eastern Black Sea Steppe (pdf), Scientific Papers Series Management, Economic Engineering in Agriculture and Rural Development, Vol.13, Issue 1, 2013.
Name of the Breed
On the naming convention and to make sure we are referring to the same breed, i.e. Racka, p.148 - emphasis mine:
Zackel is the German for the name which Linnaeus gave to a breed from another phylogenetic group of breeds, O. a. strepsiceros, (strepsiceros = zackel = straight, pointed horns), the sheep which Buffon, then Darwin called Walachian, correctly named Corkscrew Walachian (Valaşca Vitoroga) by the Serbians, wrongly named Raţca (Racka) by the Hungarians and Romanians, which means Serbian and which belonged to the group of sheep descending from the former Egyptian sheep.
Heritage
It seems to be a really old (4000 BCE) breed from the cradle of sheep domestication --Mesopotamia. It ended up in Central/Eastern Europe via north-Pontic steppes because of Thracians, at p.147 - emphasis mine:
Concerning the local sheep breeds, about which we will speak, we note that the Walachian is a Thracian sheep, introduced there some two millennia BC from Mesopotamia, where it was supposedly created some two millennia earlier. Walachian breeds, that is Romanian, group of sheep breeds was named in literature Zackel, the German name of Corkscrew Horns Walachian breed ...
Finally, there is a short discussion on paleogenetic research (pp. 146-7) but I am not knowledgeable enough to read (nor understand) so I'll leave that for someone who can.
NOTE: The author of this article is Condrea DRĂGĂNESCU (from University of Agricultural Sciences and Veterinary Medicine, Bucharest,59 Marasti, District 1, 011464, Bucharest, Romania). He has written quite a few articles on Corkscrew Wallachian. Another with specific discussion on taxonomy and the Corkscrew Wallachian is A note on Balkan sheep breeds origin and their taxonomy) (pdf). And this paper for the name Corkscrew Valachian (same author, pdf).