What precautions should be taken in working on cooling towers?

Several things. 1. Falls; 2. Skin injury; 3. Inhalation of bacteria (e.g. Legionella) 4. Inhalation of exhaust fumes; 5. High pressure injury if cooling fluid or refrigerant used and pipe damaged.
It depends. It goes with saying that you should use safety equipment to prevent falls. If you are involved in maintaince (repair, sandblasting, repainting), you should have a lead level checked periodically, as some older towers may have lead paint applied. Wear an appropriate respirators when panting and be sure your tetanus is up to date. Check with osha for more advise.