Do you know such dramas?

1. There is to be a romance between the main   characters.

2. It would be best if there was a misunderstanding at the beginning and there was a Hate-Love relationship

3. ML look older (as an actor) than FL or just be a few years older in drama than FL ( as an character)

4. It would be nice if his character was so cold

There are a lot of dramas of this type that I have definitely watched, but right now, while writing, "Memories of Alhambra" came to my mind as an example

Fated to Love You - it has everything you listed + great chemistry between the ML and the FL + the story flows nicely and I didn't get bored at all

Koi wa Tsuzuku yo Doko Made mo - apart from the missunderstanding part it has everything + the ML is really cold in the beginning and it's much older then the FL as well

Secret - this would be my first rec. The chemistry is insane and you can check all the boxes you mentioned

The Innocent Man - it has everything apart from "older ML" but I really encourage you to watch this one

About Time

Crash Landing On You

Her Private Life

Itaewon Class

The Beauty Inside