A weak upper-level impulse will pass over the Commonwealth today, producing more clouds from mid-day through the afternoon. There may be a few flurries as a result, which I've shown here in this snapshot of late this afternoon:
There is light snow falling in the mountains of southwest Virginia early this Monday morning, so I do think it's feasible to get some of those flurries surviving into central Virginia later. However, those chances are slim, and any flurries that do fall would only briefly stick on the grass or other elevated objects. This would not be disruptive for travel today.
So now our attention turns to the developing low pressure system in the southern Mississippi Valley region that will impact the Commonwealth late Tuesday night through pre-dawn Thursday as the low tracks through the eastern Carolinas and Virginia. I've taken snapshots of the precipitation type for you during this time-frame, shown below. The green is rain, the pink is wet snow mixing with rain, and the blue/white is snow.
Because of the mixing and "wet" potential of this snowfall, it's difficult to nail down expected snowfall accumulations amidst the rain, but our working map still looks like a legitimate estimate for now: