Under severe power constraints I'm considering disabling the watchdog.The MCU is to work as a stepper motor controller in a watch and drive a simple bar display too. What can the consequences be? (Project is not of DIY/hobbyist type).
The purpose of the watch dog timer is to reset the MCU should a hardware or software fault occur. It does this by generating an interrupt at certain intervals and if the interrupt does not get serviced in a specified amount of time, resets the MCU.
In general, the result of a reset mid way through your program will depend on what exact hardware the MCU is controlling and what state it is in.
For the clock you are building, I wouldn't worry about this since any type of failure will not be critical. I would say feel free to disable the watch dog timer to save power but since this is not a hobby/diy project, discuss the impact of this with your client.
The answer is found in a FMEA - Failure Mode Effects Analysis. What failures could occur? How disastrous is their outcome? How could they happen? And how likely is it?
This allows you to take the usage of your design into account. If your clock is for your wall in your garage, it will rate differently in a FMEA than if it was a clock for controlling, say, a chemical process.
The FMEA process will hopefully reveal the scenarios the watchdog should protect against. This allows you to determine if it is worth using, and if so, what specifically it should do. Many designs just toss in a watchdog because it feels good, even if the code could be totally hosed and the watchdog still thinks everything is okay. If you are going to use the watchdog, you should carefully consider what it should guard against and target its usage to that.