From the website:
The snow lion that Dorje Shugden rides on is an emanation of his fearlessness that arose when he gained victory over ignorance, attachment and hatred. This snow lion tramples enemies, the greatest ones being the afflictive emotions which arise from the self-grasping and self-cherishing mind.
Why isnt there a snow lion in the old Sakya thangkas? i dont know but perhaps a hint can be found in Music Delighting the Ocean of Protectors:
Then, having gone toward Tashi Lhunpo in Tsang,
Because of a slight inauspicious occurrence,
You immediately went to Sakya in a wrathful manner,
And were enthroned as a senior Dharma protector, praise to you!
The text then goes on the describe how Dorje Shugden made his way to Sakya, from remembering his imprints from the time of his incarnation as Sakya Pandita. Dorje Shugden then manifested himself to the then head of the Sakyas, Dagchen Dorje Chang Sonam Rinchen and proclaimed himself to be a samaya spirit of a Ganden practitioner, and requested to be enthroned as a Dharma protector. Dorje Shugden further requested for hand symbols and implements from this head of the Sakyas.
The Sakya head then proceeded to give Dorje Shugden the enemy heart, (which in current day depictions is still there, held in Dorje Shugden's left hand) and enthroned him as a protector of the Sakyas and composed rituals and prayers to him.
In Music Delighting, it also says:
In the monastery of Sakya Mugchung there are extremely vast basal substances such as a three dimensional protector palace of Gyalchen where, every year, Dagchen Rinpoche went to offer the periodic tormas, make requests and offerings. Furthermore, in most Sakya monasteries there is a tradition of performing
Gyalchen fullfilment offering ritual and propitiation, up to the present day.
So it is no surprise that thangkas of Dorje Shugden from the Sakya lineage exist, seeing that up till the time of the Great Trijang Dorjechang, Dorje Shugden was still widely propitiated by the Sakyas and their monasteries. And this perhaps, gives a hint as to why the snow lion is not depicted in the Sakya thangkas, particularly if they were drawn during the early days of Dorje Shugden where he only had the implements and ritual items given by Dagchen Rinpoche.
I would be curious to know when the snow lion of Dorje Shugden first appeared. The praise composed by the 5th Dalai Lama does mention his mounts (see below). Would anyone know?
Robes of a monk, crown adorned with rhinocerous leather hat,
Right hand holds ornate club, left holds a human heart,
Riding various mounts such as nagas and garudas,
Who subdues the mamo's of the charnal grounds, praise to you!