너무 주워!   I think you meant 너무 추워! (which means 'it's so cold!' )

저는 해를 많이 보고 싶어요! - I am not sure what you tried to say but I assumed that you meant ' I want to see sun' then It can be 해를 보고 싶어요 ! . In korean, we don't say like 'I want to see a lot' but rather say 'I want to see the sun(+as fast as it can be) '. + Moreover, you can use expression like  비가 그치고 해가 떴으면 좋겠습니다(I hope sun will come out of clouds after rain stops.)

저는 여름을 흥분해요! -May be you meant 'I am excited for summer' ?  hmmm right now I cannot come up with right phraseee but may be you can use expressions like 여름이 기다려 져요~(I can't wait for the summer) , Literally it means I feel like waiting for the summer though .

이번 여름에 많이 일하고 친구들이을 만날거예요~ 지난 오일에 비 왔어요. ㅜ_ㅜ

여름이, 빨리 와 주세요  - If you were "talking" to the summer (hehehe :) ) I would say 여름아

hope it helps .

It was closed to perfect but I wanted to make it like more native like