Sadly, the UK concept of "right of access" has long since vanished in North America. Here, land access is at the discretion of the landowner. If you don't have permission to be on their land, they can have you charged with trespassing and arrested.
This is the heart of most climber access issues, mostly due to fear by landowners that they will be held liable for injury or death on their property. There have recently been a couple of major lawsuits in Ontario that involved mountain bikers who were seriously injured while riding and sued the landowners for compensation. As a result, liability insurance rates are skyrocketing, and landowners who would otherwise be happy to let the public access their land, choose not to because they can't afford insurance, and don't want to risk getting sued.
So, to avoid having some guy become your "Mama Bear"
, your best bet would be to ask for permission before exploring any new areas, especially on private (as opposed to Crown) land.