Are discrete MOSFETs ESD sensitive?

Yes. I've used MOSFETs which had a conductive rubber band around the pins to protect the gate(s) by shorting the pins, to be removed after soldering. (TO-39, IIRC)

Any MOSFET outside of a circuit will be extremely ESD sensitive as one spike on the gate that raises its voltage above the maximum and it will be dead. MOSFETs in circuits very frequently have explicit protection (Zeners on gates or clamping diodes in drivers) and other incidental ESD protections like pulldowns or possibly increased capacitance.

More to the point of "are big (and/or) discrete MOSFETs less sensitive", they are for two reasons:

  1. The gate oxide is likely to be thicker and take more voltage to breakdown (though the input lines on an IC are probably overengineered in this manner as well), and
  2. The gate capacitance will be vastly larger, so it will take much more charge to build up a lethal voltage.

In a circuit, the more common failure modes (in my experience) are inductive spikes on the source pin blowing the gate, or those on the drain which can cause a fatal avalanche breakdown. I don't think I've ever positively identified a dV/dt failure, which is where the voltage rise on the MOSFET is so fast, the parasitic capacitances between drain-gate-source are able to turn on the MOSFET causing bad things to happen.

Nevertheless, if you ground your source well and blast the gate right at the package with an ESD gun on 11, you might be able to kill it. Users shouldn't be able to stick their grubby little hands on your gate lines because they could have just shuffled their wool socks along the polyester carpet, but if they can for some reason (???), a Zener should protect nearly everything.

YES absolutely.

I made the mistake of putting 2N7000 in my designs before and worked on them in environments that were not well ESD protected. I have destroyed literally dozens of 2N7000's doing this.

The key issue for me is "how much" protection is necessary in designs. Especially for production when adding protection costs money.