That Winter, The Wind Blows is one of my very, very favorites!!! <3333
Since you liked that one so much, I definitely recommend It's Okay, That's Love -- it has the same main male lead in it. It's an AMAZING romance drama.
Also recommend these:
The Bridal Mask
Uncontrollably Fond (currently airing, but it'll make you cry...SO GOOD)
W - Two Worlds (also currently airing, but highly recommended)
Another Miss Oh
The Princess' Man
Kill Me, Heal Me
You Who Came From the Stars
Scent of a Woman (definitely cry worthy)
The Master's Sun
The Greatest Love
Marriage Contract
I Hear Your Voice
The Reply series (1997, 1994, 1988)