When she would cough was it just once or repeated?
I'd err on the slow side, it's good for her to get out and get moving, and even good for her to cough help break up any sludge in her respiratories... but I'd let her choose the pace, at pasture, for awhile. I don't see walking as harmful, even under saddle, in short doses. Try to keep her out of dust, wet her hay if it's dusty.
It was once and she coughed two or three times and I slowed her to walk immediately and she didn't do it again. I had her on grass so I don't think it was dust. I'm trying to go easy with her but just trying to figure what easy is for her. She's different from Okie. He was sicker but recovered faster and seems completely recovered with no residual.