It would be sensible for the clothing to follow the contact arrangements, so with a holiday only contact arrangement it makes sense for the child to take their own clothes, but with a shared care arrangement the child should have clothes at both houses.
However, this won't always work due to one, or both, of the adults involve.
My kids are 1 school week night plus half all weekends and school holidays with their dad.
They have, pjs, toothbrushes, cuddly toys etc at both houses. These stay at the house where they were brought.
They also have underwear and clothes at each house, these get worn by the child and end up wherever they are that night regardless of who brought them - they belong to child the not the parent.
They have more school uniform here as they go to school from here more, we try and sort things so they don't accumulate uniform there (if they go on a Friday night they get changed before they go) but sometimes it happens and we swap it back.
All their coats and shoes are here, and 99% of the time have been purchased by me, they take what they need when they go there - be it just the shoes and coat they are wearing or more if they will need them for whatever reason.
Most sports gear, camping gear etc lives here - but goes where it is needed when it is needed.
In the holidays, summer particularly as they spend longer periods in each house, we will ask the other parent to drop off some clothes with them - it really doesn't make sense for them to have 2 sets of clothing to cover a two week period in both houses, when they are likely to grow out of them before the next time they are needed.
BUT it only works because both adults make it work, and even so I get pissed off that I buy x, y or z and only see them wear it once before they are grown out of it, and I'm sure their dad feels the same. But I know they are wearing it, just not here - and they are the child's clothes, not mine.