My DD8 started doing this around 3-6 mos old. We solved it exactly the way you joked... we stopped going shopping without her, and we let her pick out her own clothes. It just seemed like a silly thing for us to be fighting for control over.
We would veto purchases if they were too expensive or otherwise objectionable, and we would give her some boundaries to make sure she was dressed appropriately for the weather. She also made it necessary for us to declare that if we're leaving the house, pants are not optional.
Within those boundaries... go nuts. And nuts she went.
A family favorite was the outfit that featured a swim suit top over a pullover sweater. And no pants, of course.
When DD was three or four, we took her to a mountain resort in CA, and at a restaurant up the mountain we changed into our winter gear. She came out of the bathroom in tears, and the day was going to be a ruin, because she thought she looked ugly in her new snow suit. I had to take a picture of her and show it to her to convince her otherwise.
These days, DW feels comfortable buying clothes for DD on her own, because she's got a pretty good feel for DD's fashion sense.
