Q. Can I place evergreen schach very thick on the suca to keep the cold out and just leave a corner not so thick where you can see the stars? (If it rains the water would still get inside after a while).

A. Although Shulchan Aruch (O. H. 631: 3) rules that on the onset the schach should be light enough so that the stars could be seen at night, Mishna Berura (ibid. 5) quotes Darkei Moshe and Maharil. that one may place thick schach, since at least on some places one will probably the stars. He also quotes Bikurei Yaakov, that the fact that he will be more comfortable and warm with thicker schach and not be mitztaer when suffering from the cold, preempts being able to see the stars. However, care should be taken no to overly cover the suka to the point that no rain will penetrate, since that suka will become pasul, (Magen Avrohom ibid.). Maamorei Dovid (631) permits when the shiur of a small suka (seven by seven tefachim) is left with thinner schach.
Horav Shlomo Miller Shlit’a stresses that when placing thicker schach the intention when covering the suka should remain also to provide shadow and not only to insulate from the cold, since that is the essence of the suka.

Rabbi A. Bartfeld as Revised by Horav Shlomo Miller Shlit”a