Axis handle cold in the hill country really well compared to blackbuck and the African plains game like gazelles, kudu, gemsbock, etc. We have had our ranch for about 28 years and have had some cold weather in those years up by Junction. The key is they have to be taken care of by increasing feed, providing "hot" feeds like alfalfa hay or cubes or even horse and mule feed to create a lot of protein and body heat and to go out in the pasture and keep them up and moving. It takes a lot of effort and work but myself and my neighbors lost 5 axis total and one of them had a lot of age on him. Lost only 3 blackbuck between all of us. We got together and had a plan of how we were going to manage it. Total acreage was around 5,000 between us.
Blackbucks are a lot more tender to weather than axis by far.
ETA - The main issue with most of the mortalities in the hill country were on high fence ranches that were owned by absentee landowners that either did not have the knowledge of how to handle their animals in the extreme cold or just did not make the effort to do anything to help the animals. Lots of "super exotics" died along with axis and blackbucks from pure neglect. I feel pretty strong about it and don't mean to preach but it miffs me that some folks have the money to buy high fence places and fill them with animals but have no idea how to mange them or care for them. Sorry for the rant.