Since there is a threshold voltage needed to switch on a E-MOSFET, as
compared to no threshold voltage needed to switch on a D-MOSFET.....
That isn't correct...
For any MOSFET, there is always a gate source threshold voltage. That threshold voltage is the voltage required between gate and source that typically causes a small amount of drain current to be conducted. Some MOSFETs might use a drain current of 100 μA and others might use a drain current of 250 μA as their reference point. Others may use some other lowish value.
Either way, this small (but not zero) drain current is the value at which the gate-source voltage is defined as \$V_{GS(THRESHOLD)}\$.
Take the BSP29 from Infineon as an example. It is a depletion-mode, N-channel MOSFET and, in its data sheet, you'll see this: -
And, if the gate-source voltage falls more negative it turns off even more: -
And you can also see this in the table above. Look at drain-source cut-off current.
With \$V_{GS}\$ at -3 volts, drain current is typically 0.1 μA with 240 volts DC between drain and source i.e. it properly turns off with the correct control voltage on the gate. And, you can take the gate-source voltage to even more negative values. This device has a limit of -20 volts.
I would deduce that a E-MOSFET has lower noise than a D-MOSFET. Is my reasoning correct? Is there less noise in an E-MOSFET than in a
D-MOSFET, and if so, why ?
If there is "less noise" in an E-MOSFET than a D-MOSFET, it has nothing really to do with threshold voltages. Both have threshold voltages.