Is it OK to use a lower voltage to operate a relay coil than rated coil voltage?
Electromechanical relays are really current operated devices. The relay pulls in when the current is sufficient. The current is determined by the operating voltage and the coil resistance. But the plot thickens - the coil resistance is a function of temperature- the coil temperature- increasing by about 0.4% for every degree C. The coil is heated by the current through it, as well as by the ambient conditions. It is also heated by resistive losses when the contacts are carrying current. The temperature rise above ambient might be 35 C so if the temperature outside your box is 45 C, and the temperature inside is 70 C the coil could easily be running above 100 C. That means the pull in voltage will increase by 1/3. In fact high temperature versions of relays have less tolerance than the usual ones.

Bottom line is that the relay engineers designed the relay to be reliable at the nominal voltage (with a bit of tolerance for unregulated supply voltage) over a reasonable temperature range, and with rated current flowing, and to account for manufacturing variations (friction, spring constant, magnetic properties).

If you know that those assumptions are somehow conservative in your situation (say you have a tightly regulated supply) you may be able to shave a bit off, but you if you are wrong the relay operation may not be assured or contact life may be compromised due to more arcing from sluggish operation. For example the relay may not pull back in on a hot day immediately after it has been on for a while. 

Holding current is less than operating current (and contact pressure is not compromised in most relay designs) so it's sometimes possible to give a higher voltage pulse to operate the relay then back off to a lower voltage, but that's seldom worth the trouble.