Nurseries haul plants in a 'shoebox'. That is a trailer that hauls dry freight, a van. No water to move them, no cooler and this is all year long.
By the way, we haul canned vegetables in the same type van in the winter. Inside the van will not freeze the cans, in summer it will not cook the cans, tho chocolate needs refrigeration, chuckl, so the oils don't go rancid. June across the northern routes is much drier and cooler than the humid and variable southern states.
Any watering can cause damage to your roots enclosed for a long trip. IF you were hauling bananas, chuckl, we used to open the doors to allow the gases to escape so it wouldn't explode the trailer. Plants can handle some dry roots for awhile, water only if you see droop. Trees are hauled with burlap wrapped roots on a flatbed trailer