In some cultures and traditions, the equinox and solstice both begin and end seasons, but in others they mark the mid point of them (midsummer is just after summer solstice, etc). There are other terms, Imbolc is the start of spring for example, Samhain the start of winter. The Wheel of the Year might be an place to look at inspiration:
http://en.wikipedia.org/wiki/Wheel_of_the_Year