I found this on Ten Tobata's channel, except he didn't say where it was from, or even if it was official or fan-made. Anyway, my sensei, Yuki-san, hunted it down for me, without even being asked, I might add, because she's awesome like that. It's fan-made, after all. It's actually quite a sweet scene, at least this version. I've transcribed and translated the lyrics for you, which took me ages, because some of those kanji are complex, yet too blurry to make out, but I managed it eventually. As always, my knowledge of Japanese is limited, so there may be mistakes. Also, I've never watched Frozen, so there may be context stuff I've missed. Anyway, here is the video for anyone else who was looking for the Kansai/Osaka dialect version of this song. The singer also did the full song here.
Purple is Anna's lines, blue is Elsa's.
守ってもらわんでええねん。うちは大丈夫や
mamotte morawande ee nen. Uchi wa daijoubu ya!
You don't need to protect me. I'm okay!
な〜、エルサ、行かんとって、な〜
naa, erusa, ikan totte... naa!
Hey, Elsa, don't go...! Hey!
お願いや!
onegai ya!
Please!
うちから離れんといて
uchi kara hanaren toite
Don't shut me out.
そう、生まれて初めて 分かり合えるんや
sou, umarete hajimete, wakari aerun ya
Now for the first time in our lives, we can understand each other.
生まれて初めて力になるねん
umarete hajimete, chikara ni naru nen
For the first time in my life, I will be there for you.
な〜、二人で山下りようや
naa, futari de yama yoriyou ya
Hey, let's go back down the mountain together.
怖がらんといて
kowagaran toite
Don't be afraid.
一人だけ残して帰られへん
hitori dake nokoshite kaerarehen
I can't just go back and leave you here alone.
アナ。お願いや 帰りなさい
ana. onegai ya. kaerinasai
Anna. Please. Just go back
太陽は輝くとこへ
taiyou wa kagayaku toko e
to where the sun shines.
うん、けど
un, kedo
Yes, but —
ええねん。ここでは、一人やけど
ee nen. koko de wa hitori yakedo
It's fine. I'm all alone, but
自由に生きられるんや
jiyuu ni ikirarerun ya
I can be free.
私に近づかんで
watashi ni chikazukande
Don't come any closer.
それはあかん
sore wa akan
That won't work.
なんであかんの？
nande akan no?
Why won't it work?
めちゃすごい雪や
mecha sugoi yuki ya
There's so much snow.
なんのこと？
nan no koto?
What?
大阪が危機なんよ
oosaka ga kiki nan yo
Osaka is in crisis.
え？
e?
Huh?
エルサの力で大阪が雪と氷でえらいこっちゃや
erusa no chikara de oosaka ga yuki to koori de erai koccha ya
Because of your powers, Osaka is completely covered in snow and ice.
大阪が？
oosaka ga?
Osaka?
エルサなら元に戻せるやろ？
erusa nara moto ni modoseru yaro?
But you can return things back to normal, right?
いや、無理や。やり方が分からへん。
iya, muri ya. yari kata ga wakarahen.
No, it's impossible. I don't know how.
出来るって絶対できるって！
dekirutte! zettai dekirutte!
No, you can do it! I know you can do it!
そう、生まれて初めて
sou, umarete hajimete
So for the first time in your life...
ひどいわ 悲しい
hidoi wa kanashii
This is terrible, I'm miserable.
勇気を出して
yuuki o dashite
Summon all your courage.
なんもかも無駄やったの
nanmokamo muda yatta no
So everything was pointless.
二人手を取ろう
futari te o torou
Let's both hold hands.
無意味やったの
muimi yatta no
So it was all for nothing.
冬を終わらせよう
fuyu o owaraseyou
Let's end this winter together!
私にできることは
watashi ni dekiru koto wa
All I can do...
聞いて
kiite
Listen!
なんもない
nan mo nai
... is nothing
青い空を
aoi zora o
I want the blue skies...
危ないだけ
abunai kedo
But it's dangerous...
取り戻したいんや
torimodoshitain ya
... to return again.
絶対出来るって、力合わせれば
zettai dekirutte, chikara awasereba
We can definitely do it if we work together!
あか〜ん！
akaaaan!
I can't!