PSE Advent Calendar 2021 (Day 7): Don't forget the lyrics!

Question

<sub>This puzzle is part of the Puzzling StackExchange Advent Calendar 2021. The accepted answer to this question will be awarded a bounty worth 50 reputation.

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In the following snowflake-shaped crossword puzzle, 44 words can be filled in by solving straightforward crossword clues (listed below). The remaining spaces are to be filled with words appearing in a (well known) mystery Christmas song whose (partial) lyrics are reproduced below the clue list, with unclued words replaced by 'BLANK'. Line breaks have been removed from the song excerpt to disguise it further.

TASK: Fully resolve the crossword puzzle, and deduce and name the associated Christmas song.

Across (A):
3. Fruit with a tough shell (3)
19. In good physical condition (3)
23. Faucet (3)
24. Sweet potato (3)
27. Hawaiian island (4)
36. Moose (3)
43. Adhesive (4)
44. Cap, for a jar (e.g.) (3)
46. Taxi (3)
48. Parabola (3)
59. Not closed (4)
60. Apiece (4)
61. Positive response (3)

Down & Left (DL):
5. Squall, or flurry (4)
11. Small, green vegetable (3)
13. Break, split (4)
14. Cereal plant (3)
23. Noise of displeasure? (3)
29. Unit of resistance (3)
31. Domesticated ox (3)
39. Ukrainian Gunner, Luzhny (4)
41. Sphere (3)
50. Belonging to him (3)
51. Fresh (3)
54. French cheese (4)

Down & Right (DR):
1. Pale (3)
4. Numbers between 12 and 20? (5)
9. Bird’s home (4)
10. Number of seats on a tandem (3)
12. Butter commonly used in cosmetics (4)
16. Up to this moment (3)
20. Creator of Tom Sawyer (5)
22. Pair (3)
26. Crème-filled biscuit brand (4)
28. Noise of disgust? (3)
32. Veracious (4)
35. Bovine utterance (3)
37. Beer barrel (3)
42. Historical age (3)
45. Lair (3)
47. Baby's dinnertime protection? (3)
49. Vegetable, pak ____ (4)
52. Precedes 'drome', 'plane' and 'dynamic' (4)
55. South American capital (4)

MYSTERY SONG:

BLANK [30DR] [15DL] [33DL] BLANK [34DL] BLANK [8DL] [53DR] BLANK [21A] BLANK [61DL] [6DR] [62DR] BLANK [61DL] BLANK [7A] [58DR] BLANK [56A] [48DL] BLANK [30DR] [14A] BLANK [40A] BLANK [38DR] [21A] BLANK [34A] [51A] BLANK [3DL] [2DL] BLANK BLANK BLANK BLANK [18DR] BLANK [56DL] BLANK [41A] BLANK BLANK [36DL] [17A] [46DL] BLANK [58DR] BLANK [57DL] [31A] BLANK BLANK BLANK [25DL] [61DL] BLANK BLANK BLANK BLANK BLANK [50A] [30DR] BLANK BLANK [34A] BLANK BLANK BLANK [29A] [57DL] [5A] BLANK [30DR] [15DL] [33DL] BLANK [24DL] BLANK BLANK BLANK BLANK

Answer 1

The Christmas song we're looking for is:

Rudolph the Red-Nosed Reindeer, written by Johnny Marks and recorded by a number of artists.

The solved crossword:

Across (A):
3. Fruit with a tough shell (3) NUT
19. In good physical condition (3) FIT
23. Faucet (3) TAP
24. Sweet potato (3) YAM
27. Hawaiian island (4) OAHU
36. Moose (3) ELK
43. Adhesive (4) GLUE
44. Cap, for a jar (e.g.) (3) LID
46. Taxi (3) CAB
48. Parabola (3) ARC
59. Not closed (4) OPEN
60. Apiece (4) EACH
61. Positive response (3) YES

Down & Left (DL):
5. Squall, or flurry (4) GUST
11. Small, green vegetable (3) PEA
13. Break, split (4) SNAP
14. Cereal plant (3) OAT
23. Noise of displeasure? (3) TUT
29. Unit of resistance (3) OHM
31. Domesticated ox (3) YAK
39. Ukrainian Gunner, Luzhny (4) OLEG
41. Sphere (3) ORB
50. Belonging to him (3) HIS
51. Fresh (3) NEW
54. French cheese (4) BRIE

Down & Right (DR):
1. Pale (3) WAN
4. Numbers between 12 and 20? (5) TEENS
9. Bird’s home (4) NEST
10. Number of seats on a tandem (3) TWO
12. Butter commonly used in cosmetics (4) SHEA
16. Up to this moment (3) YET
20. Creator of Tom Sawyer (5) TWAIN
22. Pair (3) DUO
26. Crème-filled biscuit brand (4) OREO
28. Noise of disgust? (3) UGH
32. Veracious (4) TRUE
35. Bovine utterance (3) MOO
37. Beer barrel (3) KEG
42. Historical age (3) ERA
45. Lair (3) DEN
47. Baby's dinnertime protection? (3) BIB
49. Vegetable, pak ____ (4) CHOI
52. Precedes 'drome', 'plane' and 'dynamic' (4) AERO
55. South American capital (4) LIMA

Filling in the letters in the correct places, leads to:

BLANK [..e] [..d] [n...d] BLANK [h..] BLANK [...y] [..i.y] BLANK [a.d] BLANK [y..] [....] [s..] BLANK [y..] BLANK [e..n] [s..] BLANK [..o..] [a.l] BLANK [..e] [oth..] BLANK [u...] BLANK [..u..] [a.d] BLANK [h.m] [na...] BLANK [n....] [..t] BLANK BLANK BLANK BLANK [a.y] BLANK [..m.s] BLANK [o..] BLANK BLANK [e..] [s..ta] [c..e] BLANK [s..] BLANK [.i.h] [y..r] BLANK BLANK BLANK [w..t] [y..] BLANK BLANK BLANK BLANK BLANK [h..] [..e] BLANK BLANK [h.m] BLANK BLANK BLANK [o.t] [.i.h] [g...] BLANK [..e] [..d] [n...d] BLANK [yo...] BLANK BLANK BLANK BLANK

Then:

Realizing that [s..ta] must be 'Santa' and [..e] [..d] [n...d] (occurring twice!) must be 'the red nosed', we can gradually find more and more words:

BLANK [the] [red] [nosed] BLANK [had] BLANK [very] [shiny] BLANK [and] BLANK [you] [ever] [saw] BLANK [you] BLANK [even] [say] BLANK [glows] [all] BLANK [the] [other] BLANK [used] BLANK [laugh] [and] BLANK [him] [names] BLANK [never] [let] BLANK BLANK BLANK BLANK [any] BLANK [games] BLANK [one] BLANK BLANK [eve] [santa] [came] BLANK [say] BLANK [with] [your] BLANK BLANK BLANK [won't] [you] BLANK BLANK BLANK BLANK BLANK [how] [the] BLANK BLANK [him] BLANK BLANK BLANK [out] [with] [glee] BLANK [the] [red] [nosed] BLANK [you'll)] BLANK BLANK BLANK BLANK

This leads to the full lyrics of the song:

Rudolph the red-nosed reindeer
Had a very shiny nose
And if you ever saw it
You would even say it glows
All of the other reindeer
Used to laugh and call him names
They never let poor Rudolph
Play in any reindeer games
Then one foggy Christmas Eve
Santa came to say
Rudolph with your nose so bright
Won't you guide my sleigh tonight?
Then how the reindeer loved him
As they shouted out with glee
Rudolph the red-nosed reindeer
You'll go down in history!