...One would also think that a shipboard arboretum would be the last place onboard to have portholes that open to space, quite regardless of whether those are covered by forcefields, transparent aluminum, or plain glass.
The plants would have no use for starlight. They'd roast in the occasional bout of intense sunlight from a nearby star, though, or at least their rhythms would be thrown to chaos by the total lack of rhyme and reason in the variation in such light. They wouldn't enjoy the view, either (at least most of them wouldn't).
And if the idea was to provide the crew with a combined entertainment facility that had both parklands and starlight, why not provide the latter in a more realistic manner - by installing a fake canopy of projected stars to provide the illusion of walking under the sky of a world? If there are just a couple of portholes in the walls or the ceiling, those could just as well be viewscreens instead. That way, they'd provide more versatile entertainment.
To be sure, we've never seen an arboretum that would be open to space. That is, none of the interior sets in TOS or TNG suggested the presence of a porthole, and the exterior of the TOS movie ship was never photographed closely enough to reveal what was behind those big windows in the ship's underbelly.