The term Skythian refers not so much to a people as to a lifestyle : the Greek term Skythians and the cognate Persian term, Saka, merely refer to the horse-nomads that these two peoples respectively knew of in their time.
In the case of the Greeks (Herodotus), this meant Skythia Minor - modern day Bulgaria and Romania - where "Skythian" tribes had mingled with Thracians and Skythia Major, which stretched 20 days ride from the Danube basin, ie. to the banks of the Volga. Herodotus distinguished four tribes, but also created an artificial division between his "Skythians" and the Massagetae and Cimmerians, whilst assimilating to the Western Skythians those of Asia.
As for the Persians, they called all these horse-nomads by the generic term of Saka.
In reality, the western steppe was at this time occupied by various Iranian-speaking horse nomads, the dominant elements of which did call themselves Skythians, who probably arrived in the 8th century BC, and who were definitely raiding into the Assyrian empire in -676. Those in the northern steppes resisted Darius I in -512. They prospered, with a certain Ateas carving out a vast Skythian kingdom until its expansion was put to an end by Phillip II of Macedonia (-339). Alexander also curbed their power in Central Asia (Jaxartes, -329). The northern Skythians were then overrun c.300 by the Celts and the Sarmatians, their closely-related cousins.
In the 2nd century BC, Iranian-speaking horse nomads migrated into Bactria, Arachosia and Sogdiana ("Indo-Skythians"). They were dislodged by the Kushan, and moved to western India, where they replaced Greek rule until, in some parts of India, the 5th century.
The rich material culture left to us by the Skythians hints at a numerous and wealthy noble class. These no doubt wore armour and were richly decked out. I have used figures from Xyston's Thraco-Skythians to represent them.
Light bow-armed cavalry are the dorsal spine of a Skythian army. They can also be recycled as Alans a millenia or so later...
As in all nomad armies, those too poor or too old to ride, or those suffering from some form of social demotion (for cowardice, slave-status,...), would have fought on foot.
Troops armed with javelin and shield are represented in Skythian art. They may be shield-bearing cavalrymen, but it is equally possible that they were foot skirmishers.