Operate Arduino Nano using variable voltage
It is likely that the range of voltages that you have specified are acceptable.
However ...

The processor datasheet publishes acceptable clock speed and voltage "mappings".
Operating outside the specified ranges may lead to indeterminate operation. If indeterminate operation is acceptable to you then operation outside specification may work for you. If you are making products for customers or employers they may not be as accepting as you are.

"Brownout" is a condition which may occur when a processor is run at a voltage below specification. In "Brownout" anything conceivable may happen and a few inconceivable things may happen as well. In some cases the system cannot be reset with the external reset line and full poweroff is needed to restore sanity. To avoid this happening many microcontrollers incorporate an "anti-brownout" system which rests the processor if supply voltage enters the danger region. For a processor with a wide range of allowable operating voltages or several clock versus voltage zones, the anti-brownout trigger level can usually be user programmed to suit requirements. A brownout state MAY be triggered by a very short below-spec pulse on a power supply line. Anti-brownout detectors must be able to detect and react to any voltage dip which may cause processor mis-operation. In some cases, adding an anti-brownout function may increase the number of system rests occurring as pulses are acted on which do not in fact cause processor pro;lems. This is more acceptable than failing to detect dips which may cause problems.

ANY serious microcontroller system that is intended to provide reliable operation must use a properly configured anti-brownout system. Microcontrollers which do not have such a system should be avoided. 

The diagram below shows how to interpret the datasheet power/clock-speed mapping for one AVR processor. Whether the bounds shown are relevant to your processor can be determined from the data sheet. Familiarity with "Dirty Harry"  nomenclature will ease interpretation of the labels.