Walking is the best sensible exercise there is, so hiking is right up[ there with me. I climb our deer hill a few times each summer and never stop marveling at how great the woods are. Still, with it being private property and well watched there is always signs that others from neighboring property have been there and they seem to forget to take their crap with them. Cans, bottles, cigarette packages/butts and candy wrappers are the usual fare.
As sorry as it is, all that needs to happen is add people to the out of doors and you'll get trash left behind.
Kudos to you for getting into the out of doors with your daughter. Spark that interest early and establish the habit of bringing a plastic bag to pick up after others and she'll pass that along down the road.