The 59-year-old was helping wife Jayne onto a horse at their Cisswood Stables in Sussex on Thursday morning when another horse kicked out.
Moore, whose sons Ryan, Jamie and Joshua are all jockeys, spent Thursday night in intensive care with fluid on his lungs and damaged ribs.
"He's a bit groggy, but nothing worse than that," said Joshua Moore.
"I think he's pretty OK. He's out of intensive care. He's having a lot of antibiotics and painkillers, but he doesn't need any operations or anything like that, as far as I know."
Among the trainer's charges is Sire De Grugy, who Jamie Moore rode to victory in last year's Queen Mother Champion Chase at the Cheltenham Festival.
Ryan Moore, a three-time Flat racing champion jockey, was sidelined for more than a month earlier this year after injuring his neck at Newmarket's July Festival.
Trainer Gary Moore is out of intensive care as he recovers from being kicked in the back by one of his horses.