Head canon: Unbeknownst to Jaune, his sword is cursed and is very heavy in the hands of someone unworthy. He doesn’t know this until he watched Tyrian faceplant into the floor after trying to pick it up.
Due to growing up with seven sisters, a mother, a huntsman father, and several visiting family members Jaune was always the last to take a shower, and never had hot water. As the order of importance, as Guests, His father, His mother, and whichever sister got there afterwards.He’s taken this in good humor, as you cannot miss something you’ve never had. Yes there were multiple showers, one in the master bedroom, one in the guest bedroom, one in the twins bedroom, one downstairs, and one outside (for his dad when he got back from a hunt) but there was only one good water heater.
So at Beacon Jaune has taken to showering last in his team with cold water, something he’s come to enjoy from a decade of usage.
Jaune is also mostly immune to getting Cold shock.
A side benefit is making his teammate even more fond of him, thinking him very selfless. Jaune is unaware of this, but he is their beloved lead headed leader.
Order of Importance for showers JNPR
Ren: Hyperclean from years of trying to keep clean on the roads.
Pyrrha: Loves a good shower after a long day of intense training.
Nora: After she’s calmed down for a day and notices the dried syrup she dives into the shower.
Jaune: Doesn’t notice a wait, and occupys his time productively.