How deep do I need to sink a 6 x 6 post to support a 150 lb fire hydrant that will sit on top of it?
Even the worst of soils can support 1000 lbs/sf and there is no requirement to set something ornamental like this below frost line if you are willing to straighten it out once a decade or so.  Think about how most people do pedestal birdbaths in your area.

Now let's think of a scenario where we might want to do things a little better.  If you think someone is going to tie something to it that will induce a lateral load like the corner of a taut shade awning or your kids are going to use it to attach one end of a slackline or zipline to it..  Or maybe you want to prevent the neighborhood punks from uprooting it with their truck and absconding with it.    It these cases you'll want to go down a few feet like you are describing.  I'd say installing it like you'd do a typical fencepost in your area would handle the awning scenario.  You'll probably have to go down 3-4 feet to stop a truck.