No you can't do that. You cannot move your operating system and installed programs to an external hard drive, it has to remain on C:\ (or you will end up with a non booting pc and be in a right mess) In any case Windows will not allow you to move the Op Sys in that manner if you attempt it.
What you can do is copy your 'Documents' folder and contents to the ext hdd. (I suggest copy so that you can make sure they have copied ok before you delete anything from C:\
You have not said how big the D:\ drive is, I presume that contains your Factory Image for recovery? if so it should not be touched.