This is how I see the seasons fitting in to the months.  Sometimes plant labels break down the period when a plant blooms  to be more specific.

Month and Season

January: Mid-Winter

February: Late-Winter

March: Early-Spring

April: Mid-Spring

May: Late-Spring

June: Early-Summer

July: Mid-Summer

August: Late-Summer

September: Early-Autumn

October: Mid-Autumn

November: Late-Autumn

December: Early-Winter