I didn't know about the southerly wind and cloudy sky, but I learned this as a kid:

A-hunting we will go
A-hunting we will go
Pull up your sox and chase the fox (or whatever)
A-hunting we will go

     

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These are the verses in the Wikipedia article on the song.


A-hunting we will go,
A-hunting we will go
Heigh-ho, the derry-o,
A-hunting we will go.

A-hunting we will go,
A-hunting we will go
We'll catch a fox and put him in a box
And never let him go

(Modern versions often change the last line to “And then we’ll let him go”.)

Each consequent verse gets modified by putting in a different animal:

"...a fish and put him on a dish..."
"...a bear and cut his hair..."
"...a pig and dance a little jig..."
"...a giraffe and make him laugh..."
"...a mouse and put him in a house..."
...
Earlier versions of the song switch the words "a-hunting" with "a-roving", dating back to old roving drinking songs from the 16th century.