Camera on or off there is always a small drain on the battery as it has an LCD. If you leave it on I do believe that the meter tries to meter the scene even in the dark and will drain the battery more rapidly.
Other things regarding batteries in the F3
1
When the batteries are drained, or there are none installed in the camera, or if it fails to function normally due to extreme change in temperature, the F3 has only two settings which still can be used : a mechanical speed of approx. 1/55 sec via backup mechanical release lever(Check the
main reference map) and “T” (Time exposure setting on your shutter speed dial). All other speed settings will be inoperative, and the shutter won't fire or the reflex mirror MAY remain in the “up” position. If the mirror locks up, simply trip the camera via the mechanical speed lever again and the mirror will return to its normal viewing position. Then you can install new batteries (In the case of cold climate, use an anti-cold battery holder pack DB-2 to replace the cells or attach the F3 to the MD-4 with Ni-Cd cells). For important assignments,it is a good idea to carry an extra set of batteries with you or look at the few very good alternatives Nikon provides for the F3 users..
2
Should the battery be left in the battery chamber for a long period, insufficient contact may occur due to battery leakage. Thus, it is good practise to periodically clean the battery and the contact section in the battery chamber with a soft cloth. If the battery chamber is contaminated with a leaking battery, remove the battery at once and clean the chamber. Before doing so, try to clean and remove any deposits remaining inside, especially the clips housed inside the compartment and do a few test shots, but I would strongly suggest you get an examination of the damage done.
3
For safety reasons at home, after removal of the cells, remember to keep them away from children. Never attempt to throw them in a fire place, it may explode. In any case, the camera is not the cause for any mishap - only the carelessness of its owner.
4
Battery power falls off in extremely cold temperatures and this may cause the camera's photometric circuit to cease operating. In this situation, use new batteries and protect the camera body from the cold. Note that battery power will be recovered as soon as the temperature becomes normal. Nikon has an anti-cold battery holder pack DB-2 for this purpose, alternatively, use the F3 with the MD-4, which will overwrite the battery cell in the camera body (You need not have to remove the cell when attach the MD-4). With the motor drive attached, the camera gets all its power from the batteries in the motor drive. Thus, if you use a NiCd battery, the camera/motor drive will operate down to - 20°C.
5
Regardless of whether the camera is switched off or not, the Nikon F3 always discharges a small amount of electricity because it incorporates a quartz oscillator circuit. Further, at -10°C or below, the LCD may exhibit a slight delay in 'response time. This is natural and should not be a cause for concern. However, exposure of the camera to extremely high temperatures (80°C and above) may actually shorten the life span of the LCD (liquid Crystal Display).
Nikon F3 - Basic Camera Operations Part I