Arkae,
Assuming Art's contention that by cooling you mean inter-stage cooling using heat exchangers, then the following advantages would accrue with air cooling vis-a-vis water cooling:
1. Water cooled heat exchangers could face freezing of water at low ambient temperatures (your min. ambient temp. is -6 deg C), specifically in piping low-points and stagnant drain connections. Such a problem would not occur with an air-cooled heat exchanger
2. Fouling and scaling would be much more prominent in a water-cooled heat exchanger than an air-cooled heat exchanger
Obviously there are advantages of using water-cooled heat exchangers also:
1. Water having a much higher heat capacity compared to air would ensure that your heat exchanger is smaller in size compared to an air-cooled heat exchanger for the same heat duty.
2. If you are already having a cooling water network with certain excess capacity and sufficient pressure then the running cost or OPEX using a water-cooled heat exchanger would definitely be lower than using an air-cooled heat exchanger with a Forced or Induced Draft fan.
These are very generic guidelines and specific advantages and disadvantages for your case can only be elaborated once you furnish more details as pointed out by Art Montemayor.
Regards,
Ankur.