PM skier219 or grk for a quick answer. Both ski Wintergreen frequently and should have the best answer.
The Colonel

Closest place with least walking is down by the plunge tubing park. Locker room on the lower level too. HOWEVER, I am not sure about that ticket window and the hours or even if they sell lift tickets.

Next best is the Property Owners lot right in front of the Mountain Inn. Anyone can park there during the week.

IMHO

Snow was great today...little warmer tomorrow but Richmond schools are open again so you should have a small crowd.

Have fun.

If you already have lift tickets in hand, the best weekday parking is by the tubing hill. You can park right next to Eagle's Swoop and walk to the snow in 20-30 feet. As GRK noted, there is a restroom and locker room on the lower level of the tubing lodge.

If you need to buy tickets and can get there early enough, you can park in the upper lot right next to the Skyline Pavilion building (that's where the Edge restaurant, ticket windows, ski services office, and rental shop are located). There's also a lot just below that one that's a good backup. Either lot gets you close to the slopes depending on where you park -- the upper cross trail is on one side, and Eagle's Swoop on the other (just across the street). If you park in the upper lot, there is a walkway down the side of the Skyline pavilion building, next to the ski services office, that takes you right to the upper cross trail. Both of these lots are closed to the public on Fri-Sun, but open the rest of the time.

I'm lazy and like to access my car for breaks, swapping out skis, etc, so I always park within a short walk of the snow down near the tubing hill. It's never a problem on weekdays if you're there early enough. I usually roll in around 9am and can get the corner spot near the snow. I change into ski pants/boots/etc right at my car.

Have fun!

Thanks for the info. Getting ready to head out now.