Yes, depending on the fabric, different sarees are considered appropriate for different seasons.
For Winter, slightly thicker materials are considered more graceful. These include all types of Silk like Tussar, Muga, etc. If looking for something less expensive, Crepe material also suits the winter season.
For Summer, Cotton is the most appropriate material. Also, Chiffon and Georgette are breezy materials ideal for a hot day.
These days, materials that are in vogue are worn all throughout the year, irrespective of the weather. These include Crepe, Sico, and Georgette.