About 4 years ago, I had a very stressful October & early November, so I took a day to recoup after Thanksgiving. Saturday morning between 7am and noon, I had planned a 15 mile hike across the Sam Houston National Forest. I was going to do the "balloon" trail, except bushwack a mile and then catch a different leg of the southwest loop to get back to my truck.
I was wearing a bright blue coat & was making no effort to conceal myself. About 8:15, I rounded a bend in the creek and found myself staring at a scoped rife held by an orange-clad deer hunter, about 25 or 30 yards away. I hit the deck. No rounds fired. He immediately called out a greeting & pointed the rifle in the air. At that time, I had NO idea that hunting was allowed in SHNF. He explained that my cadence & speed sounded like 3 or 4 does, following closely together. No harm, no foul.
As far as I know, it is still allowed. But be careful! Unlike private land where pedestrians would be tresspassers, in the forest pedestrians have as much right to be there as you.