It is amazing, I just looked at the map of 610 and 45, closest big "wooded area" is about 5 miles away. But a lot of smaller areas, the Little Whiteoak Bayou is only a mile plus, a plenty of green area for deer to "camp out" in. It runs right along side and under the highway through that area.
A lot of that has to do with no real zoning laws in Houston. You have 10 story office buildings and right next to it cows, woods and deer.
A lot of that area that is wooded is natural flood areas, same as even smaller towns, in Abilene we have 4 major creeks that flow through town. Cedar Creek goes from the south city limits to Fort Phantom Lake, miles to the north. In the old days there were several small lakes dammed up along the creek in town. These areas became flood problem areas and the housing was bought and moved out. Most of it has reverted back to pasture/wooded land.
Some of those wooded areas hold some might impressive deer for Taylor and Jones county. There is one area on the south side on Cedar creek that I would love to set up a feeder and blind, but the county jail is across the creek. The city keeps the creek banks mowed to improve water flow so the area is a natural shooting lane.
Farther north about 20 blocks is where Cedar and Lytle creek converge just to the south of that is a wooded area that is well over a 100 acres, so thick in there that the city doesn't mess with. I have seen deer, coyotes and even a bobcat in that area.