Dear R.,
First, I admit that I'm not a mom, so take this with a grain of salt. Yet, I've worked with all different ages of kids. A 4-year old is certainly capable of being somewhat tidy, but she also is articulating a sense of not being able to do it. So have you looked at ways to simplify things for both of you?
For example, do you have a place for her to pile things in that is simple and easy-- something like a big plastic tub that can be closed up in an accessible corner of the kitchen and so not look messy, but not be difficult to put things into either. At 4, something which seems no problem to an adult, might truly seem difficult or too complicated to her, ie putting things away in different places or organizing them too much.
Also, as is so often told, these young years fly by. It may be a good approach to "offer up" the next year or so of "mess". By making it such a big deal, you are hurting your relationship, your temper, and your daughter's sense of trust. All she sees is that you are taking away her beloved toys. If you remove them from her too long, she will no longer want to even play with them. Children outgrow toys pretty quickly.
An approach a friend used with her daughter was when the girl misbehaved, she put the toy on a "time out". So maybe try this with your daughter. Instead of removing them indefinitely, why not give the toy a definite "time out" period of a few hours or days. Something concrete and easy to remember. If you do this consistently, she will start to grasp the concept and yet have a hope of seeing her toys again. So, let's say she won't clean up her Barbies. Well, then they will be on time-out for 2- days. (Because she probably would otherwise wait until the next day anyhow.) But then you give them back to her right away. If she still fails to put them away, then perhaps another 2-day wait. If the pattern doesn't improve in 3-tries, then maybe add a day to the "time out period".
With the paints, I would break down the tasks for her. Help her with the clean up like a kindergarten teacher. Create a big poster with the steps on it in words and pictures. So have a scisors/paper box, a paint set, and a wastebasket on this sign which should be hung near her work/play area. Then teach her to look at the sign and do the steps with you. If you are doing it together, maybe even singing a special song or something as you do it (Mary Poppins cleaning up the nursery song comes to mind), I bet she'll start to join in. Then as she masters the steps, you can back off by promising certain rewards, like an excursion or cookie, when she has them all done.
Otherwise, you are just giving the two of you headaches that neither of you want or need. Better off enjoying her than fighting with her all the time, but best to train her by helping her learn the right way to do it and giving her the attention and teaching she needs to stay on track and motivated until she learns more self-control and self-motivation (something that normally comes with age...)
God Bless,
S.