Visiting on a Wednesday in January is obviously much less crowded than Labor Day Weekend, but what if you don't have much control over when you go?
The day of the week
The least crowded times are Monday through Friday morning. Beginning Friday afternoon the people start to show up. If you are visiting tasting rooms on the weekend then plan to stop at the busier ones early in the day when they first open.
The time of day
Before 1:30 pm is your best bet. Most wineries open at 10 or 11 am. Folks tend to be at lunch around 1 pm. If you really like crowds go between 2 pm and 5 pm on Saturday afternoon.
Where in Napa, geographically
Napa Valley doesn't run a true north-south, but for the sake of simplicity lets say it does.
Highway 29 is the main road running north and south the length of Napa Valley on the west side. This is where most of the visitors and most of the wineries will be. Just a couple miles to the east the Silverado Trail runs through the valley. There are fewer tasting rooms, but there must be at least 20 of them open to the public. There are many cross roads to Highway 29 if you need to seek out someone specific over on the busy side.
The north end of the valley ("up valley" towards the town of Calistoga) will be less crowded than in the south (St. Helena to the town of Napa). The traffic through the little town of St. Helena on Highway 29 can back up for a mile or more.
Note that on a hot day it will be cooler to the south (closer to the bay). That may seem backwards, but Calistoga can be ten degrees hotter than the town of Napa.
What type of wineries
Even in the less crowded north end of Napa Valley there are major tourist destination wineries you may want to avoid during the busy times. Seek out the smaller and less well-known places.Their wines will be just as good. But if you really want that gondola ride or castle tour then plan on lots of other folks having the same idea.
Nobody likes crowds and the resulting service that comes with it so do your homework and you'll enjoy your trip more. If you really must go to Mondavi then just be sure to avoid Saturday afternoon! Or, of course, you could just come over to Sonoma County instead.