Cirno is known for her childishness (read: stupidity), so the term "Cirno" is often used instead of "baka"(バカ, fool,idiot) as a joke in the Japanese Touhou community. Apparently, even ZUN himself isn't an exception. This is because in the manual for Phantasmagoria of Flower View, she is labeled as "9. Moron" in an explanation of the game screen's layout.
Due to the infamous manual screenshot, Cirno has been nicknamed "Nine-ball" or simply "⑨".
The date "09-09-09" (Wednesday September 9 2009 09:09:09, more specifically) has been named "Cirno Day" for obvious reasons. For some reason, numerous aspects of this day everything could be translated into or connected with nine. For example: September 9 is the 252nd day of the year and 2 + 5 + 2 = ⑨, you need 9 letters to type "Wednesday" or "September", and Japan's timezone is +9. Other names for this day include "The Strongest Day" and "⑨ Day".
However, Cirno can read, unlike some of her peers, such as Mystia Lorelei. Perhaps she isn't the top idiot in Gensokyo. She can also count (she shows knowledge of rounding and fractions in Fairy Wars).
Cirno's favorite hobby is freezing a frog instantly, then watching it revive as it thaws in the water. She tends to fail one out of every 3 attempts, however, and the poor amphibian shatters to pieces.
Cirno may be over 60 years old, as she was one of the only characters in Phantasmagoria of Flower View to know instantly what was happening, declaring, "It's the festival that happens once every sixty years!" Although she was too naive to know it wasn't a festival, she appears to have been the very first character to recognize this as the year of the 60-year cycle. Even the ancient flower youkai Yuuka took until stage 6 of her own scenario to realize what year it was, while Cirno knew it from stage 1 of Reisen's scenario.