Hexproof counter on noncreature permanents
We will have to wait for the Ikoria rules update, but as of now, Hexproof is an ability that works on any type of permanent, and noncreature permanents with a hexproof counter should also have functional hexproof.

Under the current rules, Hexproof works on any permanent:


  702.11b “Hexproof” on a permanent means “This permanent can’t be the target of spells or abilities your opponents control.”


See also this Gatherer search.

I suspect hexproof will also be one of the exceptions mentioned in the Ikoria new mechanics article, and was simply missed. The fact that, according to that article, lifelink and deathtouch are going to be functional on noncreature permanents is a strong hint that the same will be true for hexproof or any other ability that works on noncreature permanents.

For clarity: Assuming the rules for ability counters are as straightforward as they could be, they will simply grant their abilities to any permanent they're on, whether or not that ability is currently relevant. Nothing in the rules stops a permanent from gaining or having abilities that don't apply in its current state. For a canonical example, Vehicles are not creatures as long as they are not crewed, but they still have abilities like flying and trample. I expect the same for ability counters that end up on Ozolith or any other noncreature permanents.