I have a cube and I want to change its pivot location. I press shift + " to go to pivot mode and while the point snapping is active , I want to move that pivot to snap to any corner of the cube but it doesn't work. So It's allowed to snap to other object but not to itself.

Any idea why can't I snap to its own vertex ?

It works fine for me.
Try right clicking on the point snap icon to see if you have any unintended settings.

This is because the cube/box node doesn't have a pivot attribute.....it just has size, centre, rotate etc.....as you observed you can snap its location to another object no problem by its "centre" but no way to adjust the pivot location on the box node.

Add a "transform" node, then adjust this nodes pivot position, rotations etc to control the location of the box the same method as you tried (insert) key or (shift+") and it will work as expected.

Couple of tips I use to help snapping objects:

"w" key for wireframe is your friend and will help greatly to hit those points that at are sometimes hard/impossible to snap too.

Right click the snap icons for properties (left of viewport) and turn on "templates" if its not on so any node you template "pink tab" you can use as a snapping object.

Hope this helps!

EZiniT
...no way to adjust the pivot location on the box node.

That depends whether you are at Object or Geometry level.

Well yes and no, So just to clarify at the "Object" level that would be editing the "container" (which does have a pivot translate parameter)....not the "box node" inside, changing transforms/pivot at the object level will move the container with it's contents but any local coordinates for the box would be unchanged.

Forgive me for stating the obvious for most, I'm certain 99.5% know this distinction already, just being clear in case there are any complete beginners reading this......I know it tripped me up once or twice in my first hours of Houdini.

Anyone saying it didn't ever catch them out at least once is not being honest, watch your back with them :^)

The split between 'object level' and 'geometry / SOP level' is certainly a 'Houdini special' - at least I don't know of any other DCC that works in the same way - and yes, it certainly caused confusion for me as a new user.