How would you store via ferrata equipment between season? Temperature, humidity? Is there any additional maintenance required?
For storing the harness, REI recommends
Transport a harness in its supplied bag and always keep it away from sharp objects, ice screws, crampons, direct sunlight, corrosive substances (e.g., battery acids, gasoline, solvents, bleach) or any other potentially damaging objects. If your harness did not come with a bag, a stuff sack can be a cheap and simple solution.
Black diamond says about the same thing.
Never store a wet or damp harness.
Store all of your gear in a clean and dry environment, out of direct sunlight and away from heat sources.
Keep harnesses and other sewn climbing equipment away from gnawing rodents and pets.
The nylon in your harness will weaken with age if not stored free from mildew, UV light, temperature extremes or other harmful agents. If a harness has been properly stored for ten years or more, retire it.
With normal use and proper care, the life expectancy of your harness is approximately three years, and can be longer or shorter depending on how frequently you use it and on the conditions of its use.
You don't want to store it in place where it would get moldy, so the less humidity the better.
For the caribineers,
According to REI,
Do not store your carabiners in humid or salty air, with damp equipment or clothing, or near corrosive chemicals.
Any slings would fall under the recommendations for the harness.