A-fib is ideally treated by rhythm control (getting your heart back into sinus rhythm). This can be done with antiarrhythmic medications (amiodarone, etc), cardioversion (shocking your heart back into a normal rhythm), or ablation of the dysfunctional electrical pathway (an invasive electrophysiology procedure). If rhythm control is not attainable, the next best thing is rate control (slowing the rate of ventricular response down to a reasonable level), probably along with anticoagulation. As stated above, anticoagulation is the real bugaboo for folks who enjoy riskier sports. Definitely let your cardiologist know that skiing is important to you, as it may help guide the therapeutic plan (avoiding anticoagulants if possible, for example).
The main concern with clots from a-fib is embolic stroke (blood clot traveling to the cerebral blood vessels), as well as embolism to the kidneys, gut, or even feet. Clots in a-fib form in the left atrium or left atrial appendage and are much more likely to go to the arterial side of things. Pulmonary embolism (venous/right heart problem) is much less likely (as opposed to blood clots from the legs) as this would require a very specific set of circumstances to occur (hole between the left and right sides of the heart e.g. PFO, ASD, VSD, etc as well as actual left-to-right shunting of clot material).