I learned Chinese in Taiwan so perhaps it is a colloquial difference, but it felt weird seeing the word 让 translated that way. I felt it was more like “let”, as in “let her dye her hair” rather than to ask. I would think 請 would have been a better word to use. Perhaps adding in a 做了之後 to make it read “春天，小草银银請春姑娘把她的头发染成银色。夏姑娘做了之後说:” to emphasize that she actually did dye her hair instead of apologizing that she can’t. This would make the English translation be “After dying her hair the Lady of Summer said:”
As for Lady of Winter being mean, I’d say they all were if they first tried to dye it and then were like, “oops, got it wrong, turns out I can’t dye it silver.”