I visited my local forest preserve recently (in a suburb of Chicago, IL) and found new signs every mile or so that read something to the effect of
Please stay on the trail so as to preserve the natural environment beyond the trail.
Part of the joy for me in visiting a piece of nature is to go off the trail from time to time, so I found this new notice a bid disheartening. This particular forest preserve is about 4 miles long and 0.25 miles wide with a small river/stream running through it, and has lots of deer within its boundaries. My initial guess about this new rule is that perhaps because of the small size of the preserve and the amount of people frequenting it, they needed to create this additional restriction to minimize the wear on the surrounding land/habitat.
After doing Google search on "off trail hiking" I found at least one national park that says it's OK to do this on their property: Off Trail Hiking. So, I now know that "hiking exclusively on the trail" is not a universal rule in the US.
My original question: How common is this rule of staying strictly on the trail for forest preserves vs. a state/federal forest park?
My updated question (based on some responses below): How to know whether it is alright to hike off-trail in a particular nature area when there is no signage saying otherwise?
Followup: The comments below inspired me to take the basic hour-long Awareness Course from the "Leave No Trace" website: Online Awareness Course. I thought it was very informative in addition to the other info on that site, and helped address my question.