Our horse carries her tail strongly to the left. She does this while out in the pasture and while ridden. When she is relaxed and just standing still it usually lays straight down but as soon as she extends her tail out, even just a little, it goes off to the side. My MIL says this is a genetic trait. A friend says this is indicative of a back/spinal issue. Lily has carried her tail like this at least 6 of her 9 years (in other words her previous owners told us she always carried it off to the side).