Why are my Rucola and Lettuce washed in ice-water?

I would suspect advertising speak. No-one these days can sell anything at all without some form of hyperbole.
We all know that rinsing salad in warm water won't be great for the leaves, so we'd rinse in cold water.
… but 'cold' doesn't really sell it, does it.

You can't sell 'just water'. Look at the advertising on any bottled plain water… it's got to be mineral, or spring, or highland, or naturally filtered, or organic, or made by celibate monks in the highest mountains of wherever* … anything except just water.

Ice-water just sounds better than cold.

*^{…or filtered through mountains for a thousand years - Best before Sept 2022 - after all, the palindrome of Evian is naive ;)}

Using cold/ice water helps crisp up leafy vegetables.