Im looking at moving to/near adelaide but I'm in need of a rural horsey suburb. Any suggestions?

This depends on what kind of 'rural' feeling you are after.

Golden Grove, Gawler and One Tree Hill will give you a slight township feel.
Piccadilly, Hawthornedene and Bridgewater will give you hills living but with a country feel.

These both offer horse-riding and other rural activities.

Check out Golden Grove, Yatala Vale, One Tree Hill, Uleybury, Hermitage, Williamstown, Cockatoo Valley etc - You can head further out to Lewiston, past Gawler to the Barossa or into the Barossa/Hills side but your commute time will increase (even with the Expressway). Closer to the city = more expensive. Further out, land parcels tend to get bigger = more expensive. It'll come down to budget.

All of these areas above have options re agistment as well as regular events, clubs etc. You do need to be aware of the fire risks in the Hills zones (including Yatala Vale, Golden Grove, OTH etc) and flooding at Lewiston etc.

Morphettville - near the racecourse, but is pricey - on the more rural side you could look at Flagstaff Hill, Eden Hills, Sheidow Park, all have horse agistment areas