Passive - Every 7th ability you cast will have increased effectiveness
1 - summer - a short beam of sunlight that travels forward dealing magical damage to all enemies hit, if this is the 7th ability cast then the ability does additional damage in the form of a Damage over time
2 - Autumn - a decent ranged dash (like cupid's) which leaves behind a trail of leaves for 3 seconds, these leaves increases ally's movement speed by a small amount, if this is the 7th ability cast, then the range of the dash is doubled and the duration of the leaves is increased
3 - Spring - a cone ability which heals all allies and very slightly knocks back enemies, if this is the 7th ability cast, then the heal is increased and the knockback is massively increased
4 - Winter - a large AOE (like anivia's ult from LoL) which slows and deals damage every second, if this is the 7th ability used, then the slow is doubled and the radius is increased
She would be played as a supporty mage - with average damage and strong utility, the idea of her passive being her ultimate gives her some versatility, if she wants to ambush people, the increased range dash or stronger slow would be better, but she could also engage on people in lane by dashing over them and using the increased knockback from spring to get them closer to her lanemate.
Any constructive critisism is appreciated :)
The cooldowns would be something along the lines of 18 seconds each, that seems like quite alot, but considering your "ult" would be on about a 36 second cooldown then it is pretty decent. This will make it so she cant just spam every ability twice, and she would pretty much have to build CDR