March is on average the driest month in Wales. Temperatures will be cool and snow is most unlikely - except in mountainous areas. That said, towards the end of the month you can sometimes get some warm days. March the 21st is the spring equinox so you can expect 12 hours of daylight and 12 hours of darkness.
March 1st is St. David's Day = the patron saint of Wales and many festivities take place to mark this day - this usually includes a St.David’s Day Parade through central Cardiff just after noon. The daffodil is the national flower of Wales and some will indeed be in flower on this day. Trees will not be in leaf.
During the last week of March and into the second week of April, you can expect to see Magnolias in flower along with daffodils and an excellent display can be found in Bute Park which is immediately on the western side of Cardiff Castle. Some trees will also be in blossom. You will also find good displays of spring flowers at this time in St. Fagans Castle & Museum of Welsh History located just to the west of Cardiff (Cardiff Bus 32).