There is no 'automatically open whatever icon the arrow is sitting on' function in Windows. There is a automatic 'jump' of the arrow to a window that pops up, but no actual 'arrow will click' on its own a icon. This is usually a sign the mouse 'clicker' inside the left mouse button is failing and the mouse needs to be replaced.
NOW *IF* you mean 'I click ONCE on a icon and it automatically opens' that is different, that would be the option 'treat single click as a double click'. A single click is "SELECT THIS", a double click is "RUN THIS". You said "whatever the icon is just happens to rest on" as in you slide your mouse across the screen, a icon is there and BOOM it SELECTS and RUNS it (does it's own double click on it's own).