Carrying a long gun with the stated purpose of "protection" is an iffy proposition.
One may carry a uncased long gun on a public way only when lawfully engaged in hunting; one may not carry a loaded long gun within 150' of a public way (it says, IIRC "Hard surfaced" but what that means is open to interpretation), as one may not lawfully hunt within 150' of a public way.
If one is carrying a long gun, and one is not lawfully engaged in hunting, then it must be "cased"; you use the term "scabbard" - now, using the current Hunter Ed curriculum as a guide (since the woods is where you may find an EPO) there is a difference - a scabbard is open, where a case can be closed.
I would be very, very circumspect in using "public" land unless you are absolutely sure that there's no problem.
I know, Massprudence.
Case in point: the Town of Framingham was thrown into a tizzy a few years back, when a person requested permission from the Town to hunt on Town-owned land over by the women's prison, as required by Town by-law (no hunting without permission of landowner). Of course, they said, "NO!" but it was a bit of a problem for a bit, as nobody had ever thought of this. If it's Water Department, or another public/quasi-public entity tread carefully.
Man with a GUN in the WOODS is a hell of a catchy headline.....
IANAL, and all that.....