Crossword Genius

I could go on horse to make an impression (4)

Ross

I believe the answer is:

etch

I'm a little stuck... Click here to teach me more about this clue!

'make an impression' is the definition.
(to etch is to make an impression in something)

'i could go on horse' is the wordplay.
I cannot really understand how this works, but
'horse' could be 'h' (abbreviation as in horse power) and 'h' is present in the answer.
The remaining letters 'etc' is a valid word which might be clued in a way I don't understand.
This explanation may well be incorrect...

'to' acts as a link.

Can you help me to learn more?

(Other definitions for etch that I've seen before include "Incribe" , "Engrave (glass/metal)" , "Chase" , "Inscribe" , "Cut design onto metal using acid" .)

I've seen this clue in The Independent.
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