IMO, with 1.5 acres, you will need to be feeding hay year round. You'll also need a way to dispose of manure, as the area is too small to just have it decompose where it sits or to harrow. So, yes, you can do it, be it will be relatively expensive and a lot of maintenence/manure picking.
The suggestions for a shelter, a sacrifice area and dividing the area are all spot on.
Do also think about where you're going to ride.