OP - in the UK your horse would indeed be called a liver chestnut , just not as dark as some liver chestnuts, but we only have "liver chestnut" or "dark chestnut", "chestnut" and "bright / light chestnut"
Thirteen, that picture of him is one of the more difficult to see his color. One thing about liver chestnuts is that they will generally lighten in color down their legs and their hair along their pasterns and coronet band will be a lighter red than their body. Here are a couple more pictures of that horse.
Chestnuts nearly always have tones of red in them. My liver chestnut pony is only liver chestnut in summer, and just plain chestnut in winter.
But I think we have different names for things over here as Sorrel is never used and liver chestnut is a common description and not just for the very very dark chestnuts shown above, so I guess it depends where you are as to what colour horse you have. We also, as far as I know, do not take into account slight changes of leg colour (as long as it is not black points making it a bay)