Speaking only for myself, food sources have always been my primary focus during late season. There are a ton of other factors that can influence things though, such as pressure, weather, wind, etc., but colder temps have often meant fewer humans and slightly more predictable deer patterns, so if there were an abundance of acorn bearing oaks around you, I'd be looking for entry and exit points to that depending on morning or evening hunt. This usually doesn't seem to happen for me until mid Dec or so.
Edit - I forgot to mention that knowing what foods they're eating is a really difficult thing to do because it there's often a wide variety to what they're eating. If you can find areas with clumps of scat, look around for what's been turned up. Look for nibbled tips of branches, berries, etc. Take pics if you are unsure, but look that stuff up cuz that's what they were eating the night before.