Many times once hunting season gets rolling, deer learn to stay away from wide open spaces during daylight hours. If you see lots of deer tracks in the fields, but never any deer, then they are likely "staging" inside of the woods in the afternoons, and coming out after dark (or vice versa in the mornings). Acorns and other tree-based food are often the preferred forage during the late fall, especially if a frost has hit the green crops still in fields.
Late season afternoons are generally when fields (that have some form of food in them) become good hunting spots again, simply because browse in the woods has been eaten or died off.
If you are the only one on the property hunting in the woods, you might be able to take advantage of the fact that many folks just like hunting in a comfy stand/box blind on a field edge and don't want to do the work of actually scouting for deer on the rest of their property. The use of food plots has made the average deer hunter less savvy about his/her quarry. They are a tool for certain times, but many use them as a crutch to avoid acquiring the skills of woodsmanship that traditional hunters considered an essential part of their toolkit.
I encourage you to avoid hunting fields until gun season has been open for 2-3 weeks, and see if you see a difference in your hunting experience. If nothing else, I think you might have more fun - there's a LOT more to see in the woods in terms of other wildlife, and you get to hunt with your ears by hearing the tell-tale "crunch crunch" of footsteps approaching during still days. My heartbeat gets a lot more frantic hearing that noise compared to watching a deer stroll into an opening from a distance.
Here's my general practice:
Early muzzleloader - hunt open woods with good food sources along terrain funnels with decent visibility, expecting to see unpressured, "dumb" deer out in the open.
Late muzzleloader/gun (on properties with pressure) - hunt woods adjacent to thickets or other security cover, expecting to see deer moving less out in the open
Early gun season (rut/chasing in my area) - hunt downwind of travel corridors to see cruising bucks, or food sources near security cover that might hold does. Bonus points for finding woods with small clearings where does may be feeding
Late gun season - hunt remaining food sources. On very cold days, watch fields with food in the afternoons