These are grammatically correct! If you're looking for more ways to say them, however, you have some different options:
1) It was so cold, I had to wear three layers of clothing.
2) It was so cold; I wore three layers of clothing.
You can also switch it around and add because:
3) I wore three layers of clothing because it was so cold.
4) I went to bed super early because I was tired.
Hope this helps!