According to several Russian pages like this one, the "pine before the gates" song is "Не сосна у ворот раскачалася" = "No pine sways at the gate".    Stravinsky later used this tune again, for a canon, "Вариации памяти Олдоса Хаксли" = "Variations in memory of Aldous Huxley" (1964).

The lyrics above for "The Larch Tree" correspond to some I found for "У ворот сосна раскачалась" = "At the gate a pine sways". The title given for these lyrics translates as "The girl and the voivod's* son":

ДЕВУШКА И ВОЕВОДСКИЙ СЫН
   
У ворот сосна раскачалась,
Наша Дунюшка разыгралась,
Наша белая расшутилась.
Воеводский сын на крыльце стоит,
На крыльце стоит — поиграть велит:
«Поиграй, Дунюшка, поиграй, любушка.
Я тебя, Дуня, лучше всех люблю,
Я платок куплю с алыми лентами,
С алыми лентами, с позументами!»
К вечеру Дуня захворала,
Ко белу свету на погост везут.
Воеводский сын на крыльце стоит:
«Прощай, Дунюшка, прощай, любушка!
От меня Дуня на тот свет пошла,
Во сыру землю, во желты пески,
Во желты пески, во дубовы доски!»

My literal translation:

At the gates a pine sways/shakes,
Our Dunyushka played,
Our fair-skinned one amused herself.
The voivod's son stands on the porch,
Stands on the porch, commands her to play:
"Play, Dunyushka, play, my dear,
Dunya, I love you more than all others,
I'll buy a kerchief with scarlet ribbons,
With scarlet ribbons, with braid!"
By evening, Dunya fell ill,
To the white earth, to the churchyard they carried her.
The voivod's son stands on the porch:
"Farewell, Dunyushka, farewell, my dear!
Dunya has gone from me to the earth,
Into the dry ground, into the yellow sands,
Into the yellow sands, into the oaken planks!"

* A voivod was the governor of a province, or the commander of an army. The adjectival form, used here, might extend to other administrating officers.


The Russian title of the round-dance movement is "Хоровод царевен"—this may help in searches for information.