Before MLP was but a gleam in some toy designer's eye, there was Fantasia. Believe it or not, one of my first sculptures was a "Centaurette" inspired by those I saw in that classic, animated feature.

That reminds me: is it just me (or coincide) or do the young pegasi and unicorns and those ponies look kind of alike?

Well, Cute is cute, all through the ages. Cartoonists tend to give their characters infant like proportions to make them visually appealing, such as large eyes, large heads, small compact bodies, and large feet and hands. So yes. The Pegasai and Unicorns in Fantasia do look a lot like the characters from MLP because the show's designers are following a tried and true method of character design. If the ponies were all sharp angles and looked more like realistic horse foals, I don't think the characters would be as visually appealing. (And far more difficult to animate.)