Maybe Washington had a Lipizzaner? It says here that Lipizzaners aren’t born white but will turn white between 6 and 10 years of age. So all that would be needed would be for the horse to be more than 10 years old.
An albino horse can survive. They’re rare, but it’s possible. Paint albinos don’t, but then ‘lethal white’ is a whole other story. However, you have to avoid leaving an albino in the sun for long periods of time because they burn like crazy, so it’s highly improbable that Washington’s white horse was an albino.
Also, most grey horses are born darker and lighten toward white as they age–Lipizzaners are just more dramatic about it. Therefore, we can assume that Washington’s white horse was an older grey.