The board has no such power. 

I am beginning to think, based on a non-lawyer reading of the DRs, that the Guideline to authorize open burning of wood in fire pits is a possible overreach by the board and might fail a test in court if an association member choose to take OPA to court on that issue.

Maybe I missed it, but can find no authority in the DRs for the Board of Directors to grant blanket exceptions such as it did on the DR prohibition against open burning of wood.

The DRs do give ECC the authority to grant

From DRs:

All plans and specifications for any structure or improvement whatsoever to be erected on or moved upon or to any lot, and the proposed location thereof on any lot or lots, the construction material, the roofs and exterior color schemes, any later changes or additions after initial approval thereof and any remodeling, reconstruction, alterations, or additions thereto on any lot shall be subject to and shall require the approval in writing before any such work is commenced of the Environmental Control Committee (herein called “Committee”), as the same is from time to time composed.

A fire pit is an improvement that requires a permit.

and now this in the DRs:

The Committee may allow reasonable variances and adjustments of these Restrictions in order to overcome practical difficulties and prevent unnecessary hardships in the application of the provisions contained herein; provided, however, that such is done in conformity with the intent and purposes hereof and provided also that in every instance such variance or adjustment will not be materially detrimental or injurious to other property or improvements in the neighborhood, the Section or the Subdivision.

Notice it references COMMITTEE, not Board. Is not having a fire pit and "unnecessary hardship?"

The fire pit Guideline may be very questrionable.

When the Board passed th firepit Guideline, I was present at the meeting. Upon adjournment, I went to board table and asked how many board members voted to allow fire pits because they wanted one on their own property. Four board members admitted that was the reason for their vote of approval.