You asked what the best snow month is in Tahoe. Historical averages
show that February typically sees the most snow, followed by January. However, in my experience, March is typically the better month to ski -- it will snow, and you'll take advantage of the warming trend that we love in the Sierra, as well as rapidly diminishing crowds.
Some additional information would be useful. Are you looking for a pure skiing experience, or nightlife as well? Do you like to ski a single mountain for a week, or flit from one to the next? What's your budget? Car or shuttles? Etc.
If you want to hit multiple hills, you probably want to do the North Shore. I've skied Alpine (obviously), Squaw, and Sugar Bowl, all of which have their charms as identified above, and from what I've heard, Rose is a really sweet hill too (and closest to the airport, assuming that you want to ski on a flight day). If I were spending six days in North Tahoe with a car, I'd spend two each at Squaw and Alpine, and a day each at Sugar Bowl and Rose. If a windy storm day came up, I'd think about redirecting to Homewood.
For a single hill for a week, with no budgetary issue (i.e., staying at the base and eating out), I'd go for Squaw.
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But the most important thing to do to maximize your time at any of these hills may be to try to hook up with locals. Much of the best skiing is not obviously best. At Alpine, for instance, some of my favorite tree skiing -- Gentian's Gully and the Promised Land -- is off Scott Chair, but those areas are poorly marked, and a wrong turn can easily leave you below the lifts. And much of the best steep and deep lines -- Keyhole, Estelle, etc. -- are accessed by a five or ten minute hike, and you'll want to know where you're going.