I second K2!!  Great choice.  

Also, I don't think anyone has recommended the Taiwanese drama MARS.  It's a bit older, but I really like it.  https://mydramalist.com/133-mars .  The male lead is a bad boy Super Bike racer (great race scenes!) who falls for a shy girl whose ability to be affectionate is marred by past trauma.   Bad boy must alter his classic alpha behavior if he wants to connect with his reclusive artist love, and his mistakes and successes on their mutual path to healing make for some deeply moving drama.  

Btw, there's a scene in MARS where the male lead pushes his girl too far too soon, with disastrous results.  Lots of people have commented how difficult that scene is for them to watch.  Wish I could remember the episode number.  Thirteen, maybe?  Just a heads up if you're not in the head space to deal with issues surrounding sexual assault and recovery.  

I think you will really like Crash Landing On You

Captain Ri is epitome of male who doesnt show too much emotion, very tough guy but is very soft and caring for the female lead. He is such a husband material ? tough but soft man, urgh ive rewatched this show so many times already its so good

lost romance            

rich man ,poor woman 

a korean odyessey  

chicago typewriter (not exactly cold hearted )

girlfriend(chinese drama coldheaarted CEO)

her private life ( this is also not exactly coldhearted )

playfull kiss

blood 

high end crush (coldhearted while funny)

innocent man (became coldhearted for revenge )

kluenchevit(thai )

forest 2020 

bride of water god 

kim kwon in he is psychometric 

secret garden 

tra barb see champoo 

memory lost  

kao waan hai noo pen sai lub 

the night of the comet 

u prince ambitious boss

khun mae suam roy (thai) 

hua jai sila

game saneaha not exactly cold

my little princess

refresh man 

sorry!! some of them are only cold heartet  but not soft  and some of them are not exactly cold hearted if any mistakes sorry 

i hope you understand!! 

thanks to you i got know dramas with this genre !!

1)Moon lover Scarlet Heart Ryeo

 This is like the perfect drama for your description !! Possessive, strong, badass ML that only shows his soft side around the one he loves (obs the FL) , he has a tough life since he's very cold hearted but deep down he's kind!!

2) Healer

This is the second perfect drama for your description !! Strong and badass Ji chang wook !!

3) The untamed

Although this is a china drama and it is bromance, trust me in the part where one of the main only opens up for the other lead!!! One of the lead is only kind to the other lead ! The chemistry is out of this planet !!

4) Love and redemption 

This drama is out of the world ! The ML is cold on the outside and so soft for the FL. He’s sooo in love with the FL !Plus he’s strong and powerful ! This is also another China drama but this drama has an interesting plot ! All the side characters are the best ! Chemistry is on point !


I personally also really love these kind of dramas too but its hard to find a perfect one ! Out of ALL the dramas I've watched, these are the ones where both leads don't do dumb stuff and make reasonable decisions. Great plots and chemistry too;))

I just watched BETTER Days (Chinese movie) it's the best movie I came across and i am still not over it. Just like your description I was also searching for such stuff and thought to let you know about this masterpiece. Hope you give it a shot. 

Mr honesty 

come and hug me

The king eternal monarch