My girls hands are still a bit too small for most store bought gloves, so a few years ago I devised a very simple thumbless pattern. My little one is in love with rainbows (she is 4) and has a rainbowdashed stuff horse and wanted me to “knit a matching rainbow”. I came upon this super cool hand-dyed yarn from etsy (knitpurlgurl) which is pre-dyed with rainbow stripes and clouds! She also has some pretty amazing self stripping pumpkin yarn.
We’ve had a bit of a heat spell in Virginia, she wore them in 80 degree weather and takes them to pre-school every morning! <3 GAH I LOVE MY 4 YO SHE IS SO CUTE!!!
free pattern – > http://www.ravelry.com/patterns/library/serendipity-mittens (hope thats okay to say!)
I also have a rainbow-loving child I made a sweater and a matching hat for her, and I know where a word “rainbowdashed” might come from 
That yarn is perfect for them.