It's in the nature of euphemisms that they can't be definitely said. I'm thinking of the Cold Haily Rainy Night versions of the story in particular. Maybe it's just my lurid imagination but I think it's there.

The DT version @displaysong.cfm?SongID=1245 is not that direct but does keep harking back to the "let him in" line.

Oh then she rose and let him in
And kissed his ruby lips and chin
And then they went to bed again
And soon he gained her favor

Then she blessed the rainy night
She rose and let him in O
-
-
O then she cursed the rainy night
That ever she let him in O

This version is less subtle http://www.folkinfo.org/songs/displaysong.php?songid=3

And she's rose up and she's let him in,
She's kissed her true love cheek and chin,
And she's drawn him between the sheets again,
And she opened and she let him in-o.

as is this http://www.traditionalmusic.co.uk/folk-song-lyrics/Let_Me_in_This_Ae_Nicht.htm

She let him in sae cannily
She let him in sae privily
She let him in sae cannily
To do the thing ye ken, jo

I would have thought the

for my head is filled with dew,
and my locks with the drops of the night.

lines relate more to the

My cap is frozen to my head
My heart is like a lump of lead
My shoes are frozen to my feet
With standing at your window

verses than Foggy Dew.

Basically, the chap is saying "I'm cold and wet and desparate for a shag. Let me in."