There's hardly ever snow on the ground (except, exceptionally, for the past month) let alone the road. Snow in March is possible but very unlikely.
Parking could be a challenge depending on how much you want to pay. There's always the private offstreet lots but these are pricey. Metered street parking is generally restricted to 2 hours or less and can run up to $4/hr (if not more) and is in effect until 8pm daily. There are also rush hour parking restrictions on main thoroughfares so look carefully at the signs.