I'd say Cirno has a bit of intra-personal intelligence just because of the trait described: "self-motivation". For one, her health is measured in that in Great Fairy Wars. She may be gutsy and bullheaded in what she does, but she recognizes her limitations when they come around.
I'd rank Cirno around here-
LowNaturalist Intelligence- She seems to have little care for the many frogs that die in her freezing games and in general seems to not hold much thought in her environment.
Logical-Mathematical Intelligence- Probably by far her weakest intelligence, unless
she really does calculate in base 9... (Danbooru, etc.)Linguistic Intelligence- Very naive and doesn't use particularly high level sentence construction.
MediumExistential Intelligence- She seems to have a sense of the passage of time, recognizing the 60 year cycle, and there isn't much of anything to imply she is much lacking in this intelegence
Spatial Intelligence- Almost a requirement for danmaku, but her's isn't particularly intricate and on at least two occasions she's had a giant blindspot right in front of her V:
HighKinesthestic Intelligence- THE STRONGEST... FAIRY. Still, being one of the most powerful of a given species is no small feat when you control ice and every other fairy seems to be able to throw an ample supply of fire.
Interpersonal Intelligence - As loud-mouthed as she is, she is also likely the strongest of her species and seems to at least be able to act as something of a leader for them when need be.
UnknownMusical Intelligence- Unless she has a secret love for Manheim Steamroller and Trans Siberian Orchestra, I have no idea what Cirno's thoughts on music are.
Intra-personal Intelligence- Nothing in her dialogue gives any clues as to her level of introspective thought is. I'd guess low if I had to. Her "motivation" seems to be something more related to outer reward than inner satisfaction in getting something done.