Let me play the devil's advocate against the reply of Voltage Spike. Therefore, this reply is intended to be challenged or debunked if it is not accurate.
Yes, mosfets drains are sensitive to ESD. If you look at the Vds spec in the datasheet, it cannot be exceeded (for the IRF530, it's 100V), even for short amounts of time.
I don't think this is accurate. Besides Vds ratings, the datasheets also present the avalanche rating, which specifically applies to situations when the Vds rating is violated. I will use the already mentioned IRF530 FET (https://www.vishay.com/docs/91019/91019.pdf) to demonstrate my idea. The datasheet shows a test schematic in the Figure 12a, where a coil is first allowed to charge up through the enabled MOSFET. Then, the MOSFET is turned off and the coil current is forced through the D-S, which will clearly violate the VDS rating and the energy stored in the coil gets dissipated in the body diode in the avalanche breakdown mode of operation.
Avalanche breakdown is the same physical phenomenon as the one employed in the high-voltage Zener / TVS diodes. Therefore, I argue that the body diode itself acts as a TVS and then, the avalanche energy must be respected to prevent thermal damage to the device.
Avalanche breakdown exhibits a very steep V-A characteristics, i.e. very small differential resistance, once it happens. Given that that standard ESD models have relatively large series resistance, I would argue that the voltage is effectively clamped by the body diode.
Example: An 8kV HBM is modeled by a 100pF capacitor with a 1.5kR series resistance. The energy stored in this model is E = 0.5 * 100pF * (8kV)^2 = 3.2mJ. The avalanche energy of IRF530 is 69mJ (more than 20-times as much). So even if the whole energy of the ESD was dissipated in the FET, it is very much safe (note that a significant amount of the energy will be dissipated in the HBM series resistance). Additionally, the avalanche energy is tested with the coil charged to 14A, which is much larger compared to the maximum current delivered by the 8kV HBM (8kV / 1.5kR = 5.33A), which means that even the peak current and power dissipation are considerably lower during the ESD event than the ones used in product testing.