There are legal answers and there are practical answers. If your custody order does not require you to provide clothing, then you probably are not legally required to.
However, would you want to go for a week long summer vacation with nothing but the clothes on your back? Probably not, and neither would your child. Even if the other parent can provide a complete wardrobe, everyone still has their favorite T-shirt or something they enjoy wearing and don't want to go without.
There is a case I know of where the parents had nearly equal time with their children. Due to disputes over who kept whose socks and so forth, the parents would put their children, with nothing but the clothes on their backs, on an airplane to go visit the other parent. The other parent would bag the children's outfits on arrival and return the outfit for the flight home. Between times, each parent maintained a complete wardrobe for each child and the children were prohibited from taking one parent's clothes to the other's house. I doubt anyone will say the children benefited from that. That has to be the guiding concern- what benefits the child.
That being said, there is frequently the parent who becomes the black hole of clothes. The kids show up with outfits but the outfits don't go back with the kids. Sometimes, it is an innocent omission because the parent is trying to launder the clothes before returning them and they start to accumulate before getting returned. Other times, it is another way for one parent to torque the other off. Either situation would benefit more from consulting a mediator or parenting consultant than litigating before a judge.
Call the court and ask to speak with a law clerk, mediation department or someone who deals with custody disputes for that court. Then ask that person you question and get your answer. Or you can call an attorney who does family law and see what the answer if from them.
I know of several courts here in Ohio that the default is the legal custodian provides the clothes unless it is ordered otherwise and some where each parent is expected to clothe the child during their times and no clothes need to be sent unless ordered.