DSD has always been free to take things she liked from our house: clothes, socks, toys, books, laptop, etc. etc. etc. Of course it caused some inconvinience over the years, but we always tried to make it easier on her.
No, we are not rich, and yes, buying an extra pair of shoes because she left appropriate ones for the weather at her mom's is not easy, but hey... she is a kid, and has little control over her family situation as it is, the least we could do is to skip the drama over "this toy is too expensive to leave the house" and "where are the socks I bought you last week, hmmm??" If she cares enough about the toy to miss it here next weekend, she'll bring it back, and if she doesn't - then it's okay.. it's her toy, she'll be the one without it, and will learn her lesson.
We discussed things like "hey, please try to come prepared for the weather, it's kind of tough buying a new pair of shoes just because you forgot the other one at your mom's", but it's one thing to discuss, and another thing to forbid. I'm all for discussing, and all against forbidding. Their lives are split in two, they are torn between two households, it's not very fair to just ask them to "suck it up, and leave it here because I bought it".
I think if clothes is of an issue, adults should take the time reminding kids "do you have things you need for the weekend? unholy socks? shoes? a sweater? great!"
Everything else is up to the kids. If DSD wanted to take a game system to her mom's, and it was HER game system, she'd have to deal with the fact that she can't play the game when she is over here, if it's fine with her, it's fine by me. IF I didn't want her to take the game over to her mom's, I wouldn't be giving it to DSD as a present, I'd be buying it for myself...
Just my 2 cents.
P.S. if DSD needed two alarm clocks and her mom refused to buy one for her, I'd be happy to provide the second alarm clock, not because it saves money for her mom, but because it puts a smile on DSD's face.
P.P.S. Teacher's salary here! hehe...