I don't know if the 39(?) restrictions apply and probably won't find out until after tomorrow(lots of cooking to do, hehe).
The law says that the 39 restrictions of Shabbat apply to Yom Tov as well, with the exception of a few.
So if its off-limits on Shabbat, its most likely off-limits on Yom Tov. That includes switching on or off electrical appliances, driving a car, going to work, handling money and writing. The major differences between the two are cooking and baking, lighting a fire from a pre-existing flame, and carrying in the public domain. All these are permitted on Yom Tov, albeit with certain restrictions.
So when it comes to exercising, we have two opinions. Rambam says that all exercise that results in sweating is forbidden. Rashi forbids any heavy exercise.
This means that everyone agrees that light exercise that won't result in sweat is permitted. However, the other scenarios are all forbidden from at least one opinion.
The Shulchan Arukh (Orach Chaim 327:2) rules like Rashi but later (328:42) rules like the Rambam. In other words, we must be strict like both opinions.
Now, what's important to know is that in the passed, running and other physical activity was considered medicine. It is considered medicine because it caused sweat, which was a healthy solution to many sicknesses. However, it is forbidden to take medicine on Shabbat (if you aren't sick), so this fell under that category.
However, what if you were simply a person who loved running, and didn't do it for the health reasons. If you truly enjoy running/jogging and truly don't do it because of the health reasons, then it would be considered permitted BUT you still can't sweat from it, because it would then be considered heavy exercise.
Here is what R. Gersion Appel writes in The Concise Code of Jewish Law (vol. 2, p. 351, n. 3):
One is permitted to go walking, but not running or jogging. Youths who enjoy jumping and running may do so on the Sabbath, as this is their enjoyment. One is not permitted to do exercises on the Sabbath that involve physical exertion and are intended to work up a sweat and tire oneself. Some permit one to follow a daily routine of calisthenics intended to maintain physical fitness. One may do breathing exercises to correct an impairment. One may use a small, hand exerciser to strengthen the hand and the fingers.