I am looking for a drama where the female lead is from a poor-middle class family background and either finds love with a super rich cold hottie or finds out she is the lost family member of some rich family and finds love there..Basically its just finding love and being from poor to rich!

Examples i have found for finding super rich cold hottie: Boss & Me

Examples i have found for being lost family member to rich family: In this case,female lead is lost granddaughter - Romantic Princess

Hello. I don't know if you've seen the korean drama  "My Princess" and "Goong". I only remember these two for now.
Mask
Fated to love you
Sunny Happiness
Boys Over Flowers :P
Dong Yi (K-drama)
Autumn's Concerto (Taiwanese Drama)
Office Girls - Watch it for the amazingly funny manager, Roy's character, and the element of hidden identity (which I love).  Just a warning though...it really goes downhill in the second half.

Honestly, I think I'd recommend an anime for this trope over anything I've seen in live action: Hana Yori Dango.  For some reason all the F4 cheesiness that had me cringing through the live actions translated much better to animation imo.  Plus....it had Mahler, Albioni, and a Michiru Oshima score 0_0
I'm scanning my drama list here and trying to give some similar dramas...

Cold, rich guy
  • It Started With a Kiss (and other versions): the main guy isn't exactly "super rich" but he's definitely cold
  • Refresh Man: I only watched the first few eps and he's not the coldest guy on earth, but he's kind of rich and kind of cold; he just likes to boss and play around with the female lead (warning: I didn't really sense strong chemistry between the two)
  • Fated to Love You: the main guy is definitely cold and rich

Lost family member of rich family
  • Easy Fortune Happy Life: the female lead is not exactly missing but more like after the rich grandfather found out about her existence, he was searching for her and eventually she lives with them (bonus: she falls in love with his rich cold grandson! XD)
  • Princess Pearl: not sure if you're up for this one because it's so old and so long but it's a periodical drama of the king's daughter; he doesn't know about her existence but she goes to find him and finds her love there

That's all I recall. I swear there are lots that fall in the "cold, rich guy" category but my mind is blank right now haha.
Thank you all for replying!! Will confirm go check them out! 
Shining Inheritance has long build up to the romance between conflicting poor girl and haughty rich boy. I really like that one, it's older but the leads had great chemistry
I second Itazura na kiss, fated to love you :)
Thanks all for the great suggestion! Have found some really good ones from you guys!:)
I think queen of ambition is  not  mentioned.she is doing everything to be rich...