Yes, campfires are most generally allowed in Corps of Engineer Parks, but only in desginated fire rings.
There are some areas where there is a county or state wide burn ban going on. In those case, it will be posted that no campfires are allowed until further notice. These notice usually are posted on the gate house and bath houses and/or bulliten boards.
If not sure-ask the attendants on duty.
We had a burn ban here in our park for about 3 weeks and then it was lifted. In the state of NM you may never see a campfire there-they are always under a burn ban!
Also many Corps parks are asking that no out-state- firewood be brought and if it is, burn all of it and leave none laying on the ground. It has to due with some kind of bugs that are killing trees that are being transported.