I suppose it will depend on what they find. My horse was diagnosed with ulcers in December. We don't usually do much in the winter anyway so, while he was on Gastroguard for the ulcers, he had a winter rest but that was more due to the time of year than the ulcers. He's been rescoped a few times since. The last time, when the ulcers were still there but healing. I asked the vet about riding and he said to just go on as normal.
In terms of the actual scope, it's just done with standing sedation which only lasts about half an hour. My boy was totally fine immediately afterwards and, although I kept him in for the rest of the day to keep an eye on him, the vet said this wasn't necessary. After the last scope, I rode the next day.