There's little difference between the earliest Scots and Irish copies of the tune (1st two below). G. Petrie in 'The Ancient Music of Ireland' said that he had noted the tune from a Betty Skillin (about 1805), but P. W. Joyce in 'Old Irish Folk Music and Songs', #427, said that Petrie's tune is one he (Joyce) had noted in 1852, and had sent to Petrie. It doesn't appear that Joyce was correct in this. The copy in Stanford-Petrie, #439, has no note as to its source, is in 2/4 rather than common time, and lacks the repeat for the chorus (given in full by Joyce, 1908, and Petrie, 1855). Both Petrie copies (with minor differences in timing between them) are in F mixolydian, and Joyce's is C lydian.
More variant is the copy of the tune in 'The Scots Musical Museum', #200, which is rather poorly engraved so I don't guarantee the accuracy of the ABC below. I suspect that this version is what was called the 'different' Scots tune.
There are two broadside ballad versions of the text in Holloway and Black's 'Later English Broadside Ballads', I, #54, "The Irish Lovers" and #66, "The Lamenting Maid". "The Love-Sick Maid" version in 'Roxburghe Ballads', VI, p. 240, is from a garland of 1765.
The 1st verse is also found in the Scots song "Mally Stuart", given from a broadside copy by D. Laing in 'Additional Illustrations to the Scots Musical Museum', #497. A traditional version of this is in 'The Greig-Duncan Folks Song Collection', I, #97.
X:1
T:THE WINTER IT IS PAST
S:Oswald's 'Caledonian Pocket Companion', bk 10, c 1759-60
Q:120
L:1/8
M:2/4
K:G
G/A/|BABd|G2gf|dBAB|G2AB|cdef|{e/f/}g2 f3/2e/|d3::\
c/B/|cdef|{e/f/}g2fe|dBAG|A2GA|B2Be|dcBA|G3:|]
X:2
T:The Winter it is past, or Curragh of Kildare
S:Petrie's 'Ancient Music of Ireland', 1855
Q:120
L:1/8
M:4/4
K:Fmixolydian
F|FD FGB2e3/2d/|cB G3/2F/F2AB|c2def2ed|(c4c2)cd|ec de f2 ed|\
cB GFF2FG|B2ed cB G3/2F/|(F4F2)cd|ec def2ed|cB GFF2FG|\
B2ed cB G3/2F/|(F4F3)|]
X:3
T:The Winter it is Past
S:The Scots Musical Museum, #200, 1788
Q:120
L:1/8
M:2/4
K:C
F3/2G/|A3/2 G/ A c|F2f d |c A G F|G2 G A| C D E|\
(fe) (d^c)|d4{BAG}|Fe c3/2B/|A c d e|f3 e/d/|c A G F|\
G2 F3/2G/|A2 A3/2 d/|(cB A G|F4{DCD}|C2|]