I think i understand your point now. I can't speak for the others but i call Cirno an idiot/stupid because she act exactly like those definitions i posted before, but i don't go so far as to say she is actually mentally retarded. There is some space between "acting stupid" and "clinically retarded"....
One more thing i want to point out:
They may be stupid, but they can't help not knowing things, even some that you'd think to be obvious.
THIS. This is exactly the problem i have with Cirno and the main reason she is my least favourite char. I can accept not knowing things, i can accept acting like a child, what i cannot accept and mark her as stupid is KEEPING DOING IT!
Small kids do act foolishly, but THEY LEARN FROM THEIR MISTAKE. After getting burned by the stove a few times, they start avoid it. After discovering that doing something hurt them, they learn to stop. Fairies doesn't have a normal concept of death but they do have a normal concept of PAIN, so they should act accordingly.
Cirno doesn't learn. She keeps going against beings that she witnessed many times are much stronger than her. For the love of God, if you take Hisoutensoku's as canon she willingly went into HELL to face Utsuho! An ice fairy going into a literal inferno..... /facepalm
If she made tons of mistakes or rash decisions once or twice i would call her simply childish. Since she keep doing it despite knowing the outcome i call her stupid.
EDIT:
From a human's perspective yes she's kind of slow, but from a fairy's perspective she's got every right to call herself a genius.
And i totally agree with this. Like i said she is probably the smartest fairy in all of Gensokyo, but she doesn't call herself the strongest/smartest while dealing with other fairies, she does so with anyone, despite getting utterly trashed by them.