Keep in mind that the number of images remaining in the display is a very conservative estimate. The more full the card gets the more accurate it is.
While deleting images in the camera can be done, there is a remote chance that doing so could corrupt the memory card. This of course would not be good. I meet people all the time complaining that their memory card is full because they didn't get around to downloading the images to their computer.
I don't use SD cards in my D800 and I always have at least 5 CF cards (1 in the camera and 4 in a card case) so I never worry about running out of memory.
Get a Gepe Extreme Card Safe to carry your spare cards. They are waterproof, crush proof and large enough that it will be difficult to lose but small enough to easily fit it your pocket or an outside pocket of any camera bag.