Well, I missed this, but really want to have my say!
With my first son I bought all color cordinated clothes for him. By the time he was 3 he would pick out a green tee shirt, green seersucker shorts and green socks etc. After he got his first pair of cowboy boot these went on with his coordinated clothing!! Or not! I have pictures after just getting out of the bath--undershorts (maybe) gun and holster, boots and cowboy hat. Both of my sons wore their cowboy boots with shorts all summer long.
When my daughter was three she went thru the summer wearing all her pretty petticoats under one dress with maybe her favorite tee shirt on top of it all. The sweat didn't bother her one bit! "Oh, what price Beauty"
My youngest son didn't care what he wore are who picked it out. (very often it was big sister!)
My grandaughter went thru the same period of outlandish garbs--dressing herself up. One of her friends in kindergarten wore the most outlandish outfits you can possibly imagine after her mother got smart and gave up the morning battle.
All adults now, well dressed and emotionally sound.
I haven't read anything on this---50 years ago we just went with our gut and our mom's advice--but I believe this is one of the ways a 3 year old can feel some control in his life. A normal healthy child begins early on to test his control over situations in many ways. Choice of clothes is --in my humble opinion--one of the easiest to deal with!
When they get to be teenagers they will go thru this again! You will really hate it then. However, I have realized that when they grow up emotionally their clothing choices will usually follow.
So support their choices in the small so the battles --maybe --wont be so hard in the big ones.
Good luck and God bless all you young mothers rearing your children in a drastically changed and threatening society. Give them lots and lots of love and don't sweat he small stuff. Too soon they are gone!