Will microcontrollers use more current on lower voltage?
There are a couple of "main" mechanisms that cause power to be comsumed in CMOS circuit: -



The mechanisms are conduction due to both P and N devices being on during transitions of input waveforms AND the charging/discharging of output/input capacitances. Charging the capacitor from Vdd puts energy into the cap that is basically converted to heat when the N channel device switches on.

The higher the supply voltage is, the more energy is wasted in the transitions of the input waveform because the conduction current is proportional to voltage and the charge energy is proportional to voltage squared.

Faster clocks mean more energy per second (power) wasted.

A third mechanism is static power loss and this is usually much smaller than dynamic losses mentioned above. It is due to gate leakage currents: -