ADA accessibility of new park anemities

To clarify, and as the OP may know
Legally, the HOA is not open to the general public. For one, this means the HOA is not subject to the ADA. But as you indicate, it is subject to the non-discrimination clauses of the Fair Housing Act. This includes a prohibition on discriminating against the disabled. What this means is that the HOA only needs to provide a "reasonable accommodation" when a disabled person requests it. What "reasonable" is will depend on the circumstances. The cost of providing an accommodation is one factor in determining whether the HOA must provide the accommodation. Cost may end up being the main factor.

Chatter
Public campgrounds are subject to the ADA. The ADA requires many such campgrounds to offer handicapped camp sites that, for one allow someone on a wheelchair to get to the grill, to the water spigot (if the campground has one), and the vault toilet (if the campground has one).

By contrast, the Fair Housing Act has no such requirements, when it comes to disability and "reasonable accommodation."

Hypothetical 1
An owner in a wheelchair asks the Board to provide a paved walkway to a picnic table, so she can enjoy picnicking on the common area with family and friends. The Board looks at the cost of adding the paving and finds it will cost $10,000. I think the Board would be in its rights to decline the request.

Hypothetical 2
An owner in a wheelchair asks for a handicapped van-accessible parking space close to the nearest HOA picnic pavilion. State and city law require a certain number of such handicapped van-accessible parking spaces, regardless of whether an organization is open to the public or not. The Board should re-stripe to provide the requested handicapped van-accessible parking space.

Hypothetical 3
An owner who suffers from severe PTSD has a companion pup. The owner requests permission to bring the companion pup to board meetings in the HOA clubhouse. The Board does its due diligence and determines that the companion pup is well-behaved and professionally certified, and that the owner does, per a doctor's note, have this severe disability. Granting permission to allow the pup at board meetings costs the HOA nothing. I think a Board would be obliged to grant this accommodation, since it is "reasonable" by all appearances.

If the Association can make the areas accessible, I think they should.

Defining what is considered reasonable under the fair housing act is the responsibility of HUD (who is tasked with overseeing the act).

Here is some info:

Reasonable Accommodations and Modifications from HUD

What HUD provides is guidelines. The courts have said much more about what is "reasonable" when it comes to "reasonable accommodation of disabilities."

I believe for a HOA/COA (a private corporation) to comply with what public institutions must comply would be exorbitantly expensive. When it comes to disability accommodation, there's a reason private corporations do not have to meet the same, very high standards as entities that serve the general public.

A judge could also rule that a HOA's covenants do not authorize many of the modifications that public facilities are required to have.

In other words, a board should not be spending money that the covenants, city, state and federal law do not authorize.

I support reasonable accommodation of the disabled. When the cost to a HOA is prohibitive, then the accommodation is no longer reasonable. My recollection is that the courts tend to agree.