Yes, winding a watch is a reversible process.
Reversible process:- It is a process which can be made to proceed in the reverse direction by a very slight change in its conditions so that the system passes through the same states as in direct processes, and at the conclusion of which the system and its surroundings acquire the initial conditions.
All isothermal and adiabatic processes when allowed to proceed slowly are reversible, provided there is no loss of energy against any type of resistance like friction and viscosity.
In the case of winding watch, if we make a small change in the system; by reversing that change, the system will return to its original configuration. That is why; winding a watch is a reversible process. Apart from this, all the other given phenomena are irreversible, because if you make a small change in the system, the system will not return to its original conditions.