Hello,
One of my all time favorite tunes is the russian По́люшко-по́ле (Polyushko Polye), it is of course not written for a whistle, but…
…Is this tune playable on a tinwhistle at all? By moving and changing things?
(there are many different versions of the sheet music)
Oh sure, it’s playable. This particular transcription is effectively in Bb minor, despite the key signature that makes it look like Bb dorian.
If you don’t need to preserve the concert key … Mentally substitute a key signature of 2 sharps instead of 4 flats. Ignore the the Gb accidentals, and change the A-nat accidental to A# (to be cross-fingered or half-holed). And voilà: just play it as written on a D whistle. It will come out in concert B minor and sound fine. So:
X:1
T:Polyushka polye
M:4/4
K:Bm
d4 B2 d2|c4 A2 F2|dcBA B2f2|c4 F4|
B2AG FEFG|F2 c2 ^A2 F2|BBAG FEFG|F2 c4 f2:|
If you have a Db whistle (rare), use that instead of a D whistle, and it will sound as originally written in Bb minor.
If you have an Eb whistle, transpose the notation down a half-step to Am and play that. You’ll have a G# and F-nat to cross-finger or half-hole:
X:1
T:Polyushka polye
M:4/4
K:Am
c4 A2 c2|B4 G2 E2|cBAG A2e2|B4 E4|
A2GF EDEF|E2 B2 ^G2 E2|AAGF EDEF|E2 B4 e2:|
Of course, these transformations also apply to the second (harmony) part as well as the first.
Looking at that last bar, not to mention bars 2, 3, 4 and 6, wouldn’t F phrygian be more accurate?
How often do you get to say a tune is in F phrygian, after all?
Nope. The simpler analysis is that it’s a conventional i - iv - V - i harmony that ends on a hanging V cadence, which is resolved back to i on the repeat.
|i - V - i - V | iv -V - iv - V 
MTGuru, many many thanks for this extensive response.
As a relatively new whistle player I wouldn’t have been able to do this on my own.
I will try it on a D whistle later today (otherwise they will go crazy at work 
)
EDIT: how do I crossfinger a A#? I know how the half holing technique.
Is there a crossfinger chart?
In my experience A# is usually half-holed using an XDO OOO fingering, where X is a covered hole, D is a partailly covered hole and O is an open hole.
You can also try to use a cross-fingering of XOX XXX which works better on some whistles than others. It may come out sounding too flat on some whistles.
Since the idea is to flatten the Bnat you can try any combination of holes covered below the open TH2 hole to see what works best. Try XOX XXO or XOX XOO and other combinations.
Half-holing always works. Half-holing is a useful skill to develop. So if you have not done that already use this tune as motivation to do so.
Have fun. Enjoy the music.
Feadoggie