No, because "the moonlight feels cold" means that you TOUCH the moonlight and it's cold to your touch. The first sentence would be the right way to say it.
TO FEEL COLD = STH IS COLD TO THE TOUCH
- Your hand feels cold because it's snowing outside.
- The top of my car feels cold.
TO MAKE YOU FEEL COLD = STH IS COLD SO IT MAKES YOU COLD AS WELL, BUT YOU DON'T HAVE TO TOUCH IT NECESSARILY
- The lake makes me feel cold.
- The snow is making me feel colder.
I hope this was helpful!