I have been on Coumadin/
Warfarin for at least 10 years, more I think...
and have never had a problem with running or bike riding, or using my table or radial arm saw, or a chain saw.... When I accidentally cut myself, always minor, I think it bleeds a bit more than if I had full coagulation, but I've never had trouble stopping the bleeding. I also do not have much trouble maintaining the correct INR range of 2 to 3.