Their year cannot be solar-based unless they have some mysterious factor which causes the seasons. (Which could be the case, because their seasons are of variable length.) But without a mysterious factor, we assume that their seasons are caused by the solar cycle which would imply that a solar year would have a correlation with seasons. Clearly, it doesn't.
But, I do like the lunar calendar idea. It's better than my brother's idea that a group from our world in the future was transferred to another world with different physical rules from ours. In that world, they forgot all future technology and reverted to feudalism but still maintained the calendar system.
On another note, does anyone know how the harvest cycle works in aSoIaF?