The different systems have slightly different names for the seasons.
In no particular order:
(and anything left out is purely a google search oversight on my part)
12 Tone Pictures (examples) - Reveal Consultancy:
True Spring, Bright Spring, Light Spring
True Summer, Soft Summer, Light Summer
True Autumn, Soft Autumn, Dark Autumn
True Winter, Bright Winter, Dark Winter
Truth is Beauty - Seasonal Color Analysis:
Warm Spring, Bright Spring, Light Spring
Cool Summer, Soft Summer, Light Summer
Warm Autumn, Soft Autumn, Deep Autumn
Cool Winter, Bright Winter, Deep Winter
12 Blueprints: Christine Scaman (Sci/Art):
True Spring, Bright Spring, Light Spring
True Summer, Soft Summer, Light Summer
True Autumn, Soft Autumn, Dark Autumn
True Winter, Bright Winter, Dark Winter
Seasonal Color Analysis: The Chic Fashionista:
Warm Spring, Bright Spring, Light Spring
Cool Summer, Soft Summer, Light Summer
Warm Autumn, Soft Autumn, Deep Autumn
Cool Winter, Bright Winter, Deep Winter
Pretty Your World: Color Revival by Lora Alexander:
Warm Spring, Clear Spring, Light Spring
Cool Summer, Soft Summer, Light Summer
Warm Autumn, Soft Autumn, Deep Autumn
Cool Winter, Clear Winter, Deep Winter
Seasonal Color Analysis Blog, Yelena Starikova:
Warm Spring, Clear Spring, Light Spring
Cool Summer, Soft Summer, Light Summer
Warm Autumn, Soft Autumn, Deep Autumn
Cool Winter, Clear Winter, Deep Winter
Shop My Closet Color Guide:
Warm Spring, Clear Spring, Light Spring
Cool Summer, Soft Summer, Light Summer
Warm Autumn, Soft Autumn, Deep Autumn
Cool Winter, Clear Winter, Deep Winter
Color Me a Season:
Absolute Spring, Pastel Spring, Striking Spring, Glorious Spring
Absolute Summer, Moonlight Summer, Sunshine Summer, Indian Summer
Absolute Autumn, Gentle Autumn, Golden Autumn, Striking Autumn
Absolute Winter, Snow Frost Winter, Firelight Winter, Sunset Winter