Cold guy softens up after meeting the female lead?

A good example would be 4th prince from Moon Lovers.

I don't want him to be cold and indifferent because he lost  or got dumped by his first love.

Hana yori dango
Something about 1%
Heartstrings
Love Contract
Marriage, Not Dating
Mars

Sekai Ichi Muzukashii Koi

i think theres a lot, but these just what i can think of:
something about 1%, my secret romance, drinking solo, personal taste, oh my ghost, she was pretty, boys before flower, rich man poor woman (jdrama)