there was a Midge in a Barbie and Midge 50th anniversary gift set. she had on the
"Luncheon on the Terrace" outfit. it was a dress with a multi colored polka dot top, with a green and white check skirt, that had a matching wide brim hat, and she had red hair. as far as the pink coat goes, well the Barbie in the set had a pink pantsuit with a fuzzy looking pink vest. and the pair came with a tea set. I just saw it on "doll peddlar" for $99.99
the Midge sounds like what you described, minus a pink fur coat.