Since cow is one of the sacred animals in Hinduism, are there any cremation rituals that need to be followed when a cow dies? If yes, what is the exact process?
I am not sure how you got the idea that a cow should be cremated. To be frank I have never found (so far) a reference which says that a cow should be cremated or even buried. So, there seems to be a complete lack of references regarding this topic in the scriptures.
However, in ParAshara Smriti, there is an entire chapter dedicated to how to serve the cows. This is the 9th chapter of the text and is named " Go Seva Upadesha Varnanam" (Instructions regarding how to serve the cows).
The verses given below are all from that chapter:
On breaking a horn, a bone, or the spine about the waist, if the animal lives during the next six months, — there is no penance prescribed by law.
On causing a fracture or a wound, the sinner with his hand must apply some oily substance to the injured part ; fodder also must be given to it, till it is restored to full strength,
The man must nurse it, till its entire body is rendered whole ; and then, in a Brahman's presence, he is to make obeisance to it, and bid it farewell.
Verse 21 is important for us. To understand what it actually says we need to see the original Sanskrit verse:
The 2nd half of the verse is important for our purpose and which transliterates to -
Gorupam brAhmanas agre namaskritvA visarjayet ||
Now, Visarjana means to offer something unto water. So, the dead cow should be submerged in water (possibly in a river). No cremation or even burial is ordained.
NamaskritvA visarjayet -- It should be first offered respect (by doing Namaskara) and then the body should be immersed in water (Visarjayet).
And, this is actually what happens too from what I have seen. In Ganges, for example, we often see the dead bodies of cows/bulls being floating carried away by the current.