The example I always point to is the bust of Washington, but Jean-Antoinne Houdon. The bust, which Washington and his family both considered excellent, depicted the look on Washington's face when someone tried to overcharge him for a horse he wanted to buy. The bust is not quite sneering, but has a certain haughtiness and indignation about it.

Firstly, Washington was a member of the Virginia planter class. This put him at the financial apex of American society, and carries with it certain assumptions. He certainly expected to be deferred to by his social lessers, and famously complained in his private letters about the egalitarian leanings of the New Englanders he was to command when he arrived at the siege lines around Boston in 1775. Whenever he was in Virginia after rising to fame and power, he certainly played the part of the social grandee, extending hospitality and credit to more-or-less all comers.

We can fairly say that Washington was ambitious. While he and Martha certainly seemed very much in love with each other, it cannot be a coincidence that Washington married a wealthy widow. He was a major shareholder in the Ohio Company, a land-speculation firm with designs on the Ohio Valley. Washington's connections with this company secured him a commission as a colonel of the Virginia militia, the command that he held when leading the mission to the Forks of the Ohio that started the American chapter of the Seven Years' War. It is likewise not an accident that he wore a military uniform to Congress on the day that body was debating who should command the Continental Army. When he agreed to serve as President of the Constitutional Convention, he also had to have some inkling that he would be the natural choice for the national executive the new Constitution would create.

With his military "family" and allies, Washington was a loyal supporter and patron. His chief aide-de-camp during the war, Alexander Hamilton, became Washington's secretary of the treasury and political majordomo. Henry Knox won Washington's undying affection for bringing artillery across the frozen wilderness to the siege of Boston, and rode that favor to increasingly high command during the war and an appointment to Secretary of War afterwards. Washington, who never had children of his own (he was probably rendered infertile by a case of smallpox he had when he was younger), seemed keen to "adopt" the remarkable young men who entered his orbit, like Hamilton and the Marquis de Lafayette. His relationship with the latter, in particular, was noted by him, the Marquis, and observers to be exceptionally paternal.

Blowups like he had with Lee were pretty rare. Excessive displays of emotion by men were considered unfashionable in Washington's Stoic-influenced time (this is also why the story of him dropping to his knees in the snow at Valley Forge is probably bullshit). Many of his letters and orders from the war contain subtle discontent, if not exasperation, at the behavior of the men under his command, but there are few accounts of him shouting at or personally striking soldiers, a la Patton in WWII. The Lee incident was the result of Lee very nearly dealing a fatal blow to the army's morale after the hard winter at Valley Forge through a mixture of (possibly malicious) stupidity and cowardice. Lee had been angling for Washington's job almost since the start of the war, so there was also a personal dimension to the affair.

This is not to say that Washington was incapable of cruelty. The man was, after all, a slaveowner, and one cannot divorce slavery from the master's willingness to beat, maim, or kill people for defying him or costing him money. As president, Washington lived in Philadelphia, which had a gradual emancipation law which granted freedom to any slave that lived in the city for more than a few months. Washington carefully rotated his slaves between the presidential mansion and Mt. Vernon to make sure that no one earned their freedom under this law. Washington also enforced corporal and capital punishment in the Continental Army, approving of the flogging and execution of hundreds of American soldiers during the war. This was accepted at the time, but does require a certain hardness to see through.

Sources: Fitzpatrick, ed., The Writings of Washington

Visits to and conversations with staff at Mount Vernon, Independence Hall (also preserves the site of the Presidential Mansion), Valley Forge, and a number of other sites related to the American Revolution.