As in my state, there is nothing written in stone on this. It is up to a judge's interpretation.
Here is how it can happen, and maybe you recognize yourself in one of these scenarios:
1) You, the custodial parent, send the kids with a suitcase full of clothes. Dad decides to be a pain and doesn't send the clothes back.
2) You don't send the kids with clothes and he has nothing for them to wear. If you send clothes with them and he will return them, you're better off doing that. If he doesn't return them, then he can buy his own clothes for the kids.
I'd hate to see you go to court over clothing but people do! It's such a waste of money though. It's something you and he should work out. It's not written into statutes, so it's a matter of how states have interpreted it, and they all interpret it the same. They want mom and dad to figure it out between themselves.
So it really depends on how cooperative he is. If they have enough clothes to wear, they can pack a bag and bring it to his house but you have to insist that the clothes come back with them.
Fighting about clothes, on his part, is just his way of trying to get control over you. It's terrible but it happens a lot. See if you can avoid this situation and work it out with him.
The one thing that you do not have to do is provide receipts. He probably just wants to make sure you're not taking expensive vacations to Europe or cruises or something outrageous, although you have the right to take the kids where you want, I'm sure.