However, if you actually look at the operating voltage for the MCU used in UNO, it says
"operating voltage: 1.8V - 5V"
So I was wondering if its okay to use UNO with lower supply voltage.
Of course, if it is connected to the USB for programming, it will be powered by 5V via the USB cable.
I am mentioning when the UNO is just running the firmware programmed into it without any USB cable attached to it. (for example, connected to a Li-Po battery that would probably give a supply voltage around 3~4V)
Has anyone tried this before and checked if UNO still works well?
One of the factors to consider at a reduced voltage is the clock frequency - notice the "Speed Grade" line in your specs. Not sure what other changes they make, but at least for the Pro mini (same processor), the 5 volt version runs at 16mhz and the 3.3 volt version runs at 8mhz (they change the regulator and the resonator on the board for the different voltage.
The Uno board has a 5V regulator on-board, which is why it runs at 5V. The standard programming for
an Arduino 328P DIP package has brown-out detector set for 2.7V which is a little close for comfort for
running at 3.3V (brown-out detector resets the chip if the supply drops below its setting). I think the
3.3V Pro Minis set the brown-out fuses to 1.8V limit.
In practice you will likely get away with 16MHz and 3.3V, but its definitely outside the spec of the
chip (across the full temperature range). 4V is OK I think, but you need to check the voltage
regulator doesn't throw a wobbly at being back-powered like this (this may depend on the precise
version of the board). Somewhere on the datasheet there is a graph of clock speed against supply
voltage.