Get a bigger SSD (I suspect the limited space is your real problem).
Moving the OS to the HDD is technically possible, but very complicated and it is VERY easy to mess up completely.
But you DO NOT want the OS on the HDD. Not just the boot-process, but EVERYTHING will slow down noticeably.
Believe me: If you got used to an SSD as C: drive you'll never want to go back to a HDD. (Despite your "I don't mind the slower boot" remark. You'll WILL mind.)
Replacing the SSD with a bigger one (migration software is often included with the SSD) is a lot easier to do and will not have the "lack of performance" draw-back.