Deer behaviour definitely changed with the H&H update, and they are indeed easier to hunt now. I also found it a bit disappointing, as they were never difficult to hunt in the first place as long as you used a bow/spear or sneak and a knife.

They used to run away they second they became "alerted" (the red exclamation mark) but now they, more often than not, just stand there for at least a couple seconds.