I rent a two story house in Pennsylvania, my driveway is 1/8 mile long (asphalt)which requires being plowed and salt distribution. I currrently don't have a lease, who's responsiblilty is it to keep driveway clear?

No one's, if it's not in a lease. So that means you if you want to get in and out, sorry.
Homeowners are responsible for sidewalk areas used by the public.

I would say it's the landlords responsibility, unless you were told when you moved in that it would be your responsibility to keep it clear. Phone somebody in your state about the Landlord/Tenant Act. The mailman(if Applicable) needs access to the house. What if you don't have a car so you just shovel a path to your house and it catches fire. How are the fire trucks suppose to make it through 3 feet of snow?

Look in your original lease. The terms of the original lease continue (except for expiration and rental). From my research this is not dictated by statute, but as part of the landlord/tenant agreement. The property owner IS responsible for clearing publicly accessible areas like sidewalks. But a driveway is private. So you need to negotiate this if its not in the lease.