So basically...
Cirno was fed up with the many times Suwako defeated her for freezing random frogs, so she pushed Suwako into the lake when she wasn't expecting it, and then lake froze over. Then when it unfroze in the spring, Lily discovered the corpse of Suwako?
Or was she freezing frogs again in this scenario?
If so, did she lure her toward the lake, then throw her in the lake?
Are there more details to this that we're missing?