What is "dead"s grammatical function?
1. As an adjective modifying "my horse" if the situation is that the horse was suddenly dead while running in his tracks.
2. As an adverb modifying "stopped" if the situation is that the horse suddenly stopped while running in his tracks.
3. Either 1 or 2 according to context
I think the correct answer is 3
This is dictionary stuff. Have you looked?
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"dead in one's tracks" is an idiom. The horse did not die.