It's somewhat about control and somewhat about not knowing how to make sound choices...she's 3. My daughter was this way at 3, too. Then my granddaughter...the things I learned that worked with both were:
~ If you take her with you let her know whatever she picks out she WILL wear. If she then flat out refuses and will not then return it that day or the next, and don't get something to replace it, her consequence is she loses out. This is where not knowing how to make sound choices comes in, maybe she did like it in the store, but seeing it at home she doesn't. So, you help her by:
~ Simplifying her wardrobe. Does she like leggings, jeans, skirts, what? Buy only solid color bottoms in the colors and styles she "likes" and will wear, in as simple a style as possible. Leggings and jeans, that's all you buy. Skirts only? That's all you buy. This way you pull out a bottom, she then has her choice of a top from 2 to wear with it. My daughter would only wear jeans for awhile, so she had about 10 pair the same, the only variation was the shade of blue denim. My granddaughter would only wear leggings, black, even in summer, so I bought black bike shorts, she wore them. If you have a child like my granddaughter who would only wear leggings and t-shirts life is bliss, she would bathe, dress in the next day's t-shirt and leggings, and go to bed, waking up dressed in the morning :)
~ This is where the cuteness comes in, buy cute tops in colors to coordinate with the bottoms she has, stick to plain styles if that's what she prefers. Say, all her bottoms are in pink or purple, you buy only tops that have pink or purple in them, preferably both colors so they go with all her bottoms. Since my daughter would only wear jeans and loved pink and purple that's what her tops were. My granddaughter, everything went with black, especially if there was any trace of black in it.
When you simplify the choices she has by coordinating the colors, she'll always be color-coordinated, but still retain some control since she picks the top :)
~ Do the same with jackets, hoodies, buy only colors to match the tops and bottoms she has, then they coordinate. My daughter had denim jackets for years for mild weather, purple or pink winter coats. Her shoes and boots were pink and/or purple as well, or a neutral tan, we always received compliments on how well-dressed she was, so I know this works.
~ Buy socks in only one or two coordinating colors so they go with everything and her choices aren't overwhelming.
~ You can add pizazz to her simplified outfits with jewelry in coordinating colors. A couple of necklaces and bracelets to switch around to start.
~ By now you may have realized it's not in your or her best interest to take her shopping with you, too much eye candy for her. Either go alone or become friendly and familiar with the online stores you physically shop at. I do this with my little guy (4 next month), I order from Crazy 8, Old Navy, etc., during sale and clearance times. I coordinate his stuff, too, though he isn't picky he is always coordinated, in blues or browns.
Once you balance her choices and control, which she still has but is limited to minimize conflict, it will be easier on the both of you. Plus she'll look like you want her to, coordinated in cute, if not super cute, outfits. Do this as long as she stays particular, it will get to be a habit and the frustration it saves is priceless. BTW, fashion consultants recommend the same thing, coordinate 2 or 3 basic colors so your whole wardrobe goes together, see a top you like buy it in all the colors you wear.
Hope this helps!