When I was on Lovenox (sp?) injections they really did a number on me with the bruising. Thank goodness I only had to be on the injections for a few days!
No biking or jogging or such during that week. (no nose-blowing or eyebrow plucking, either!)
Now that I'm just on low-dose aspirin to keep clots at bay, I can do whatever I want.
Do make sure the docs know what your regular activities are if they put you on clot-busters (the heavy-duty short term stuff). For clot-free maintainence type blood thinner drugs you should be fine.
"If Americans want to live the American Dream, they should go to Denmark." - Richard Wilkinson