You could write the XmlDocument to a MemoryStream, and then Deserialize it like you already did.
XmlDocument doc = new XmlDocument();
ClassFromXsd obj = null;
using (var s = new MemoryStream())
{
doc.Save(s);
var ser = new XmlSerializer(typeof (ClassFromXsd));
s.Seek(0, SeekOrigin.Begin);
obj = (ClassFromXsd)ser.Deserialize(s);
}