Here in Australia it seems that the most consistent place to find horse agistment properties is on gumtree.com.au.

Just select your local area and then type horse agistment in the search box. Once you find a property you think is appropriate, be sure to go and pay them a visit, see what the facilities are like and ask them exactly what level of horse care they will provide. For more information on What To Look For In A Horse Agistment Property, see my post here.