Old horse reverses to and fro unsteadily, due to this? (7)

'this?' is the definition.
I know nothing about this answer so I cannot tell whether it can be defined by this definition.

'old horse reverses to and fro unsteadily' is the wordplay.
'old' becomes 'o' (common abbreviation eg in OE for Old English).
'horse' becomes 'h' ('H' can be a synonym of 'horse').
'reverses' says the letters should be written in reverse.
'and' means one lot of letters go next to another.
'unsteadily' indicates anagramming the letters.
'o'+'h'='oh'
'oh' written backwards gives 'ho'.
'to'+'fro'='tofro'
'tofro' anagrammed gives 'ofrot'.
'ho'+'ofrot'='HOOFROT'

'due to' acts as a link.

Can you help me to learn more?