You're talking about 1,400 kms of Camino from the Mediterranean coast to the north eastern corner of Spain, so one can only describe in broad terms:
Winter - Temperatures on the Mediterranean coast are temperate but within a few days you are walking at altitudes over 1,000m at the foot of the Sierra Nevada mountains. You can expect snow and cold. After Granada, altitudes are lower and the climate is a relatively mild but wet around Cordoba to Merida. From Merida, you follow the Via de la Plata north, with higher altitudes on the way to Salamanca. Here you can have severe winter conditions. Similarly on the Sanabres after Zamora, you should be prepared for the worst.
Spring - Landscapes in the south are green and lush. If you're lucky you'll see orange or almond blossoms. Probably the most attractive scenery of the year in Andalusia. Some of the rivers can be in flood, so you can expect to get your feet wet in some places. Still potentially very cold (snow in April this year) at the higher altitudes near Granada and on the Via de la Plata near Salamanca. By the time you join the Sanabres, things may be warming up even in northern Spain.
Summer - Do not attempt unless you are experienced at walking in extreme heat. The route from Almeria takes you through Europe's only desert. Then, on the long days walking through olive groves around Cordoba you will experience daily temperatures over 40ºC. On some stages (e.g. Alcaudete to Baena) you need to carry your full supply of water for 24km with no settlements between towns. On the Via de la Plata you face some long stages where walkers have died of heat exhaustion in the last years.
Autumn - From mid- or late-September, temperatures become manageable again. You will still experience hot days at the start. Landscapes in the early stages tend to be brown and dry. Rivers are dry. If you're lucky, you'll be wearing shorts until Merida or later. On your way north on the Via de la Plata, you'll notice a sudden shift to a northern climate - perhaps on the climb up to Fuenterroble before Salamanca. By the time you reach Zamora, you'll need a three season sleeping bag to cope with the unheated albergues.