In other words can one seek payment for damages to personal property left on public land?
I suspect this falls into a very gray area. Each case would probably have to be judged on the individual merits of each case.
For discussion, say the public land involved allows primitive camping for which no additional fees are collected nor are there designated camping sites. One erects an expensive tent and associated high dollar camping equipment. One leaves for the day, for what ever reason and comes back every evening to spend the night. Is this any different then the fella who erects a hunting blind, spends his days there and goes away every evening?
How about if the person leaves for a longer period and comes back say only on the weekends? How about if he is gone for a month before returning?
Certainly some one leaving for the day should have a reasonable expectation that his property is secure as is. Leaving property unattended for a longer period might be considered abandonment.
How about a person leaving un-attended property on a public street? Isn't this essentially what one does when he parks his car on the street? In this case, if the property were to be destroyed or vandalized, one would simply seek restitution from your insurance carrier and let the authorities take care of the rest.
Again, in the case of the camping equipment, one would make a claim with his home owners policy for restitution. (ignoring deductibles for sake of discussion) I believe most policies cover your possessions while "off premises". Granted, there may be limitations, and the value of your "well constructed blind", may exceed the normal "off premises" limitations.
I guess my conclusion would be; If I can purchase insurance to cover the said circumstances, then yes I would also expect to be able to successfully seek restitution thru a small claims court. So,,,,,,, maybe pose the question to an insurance agency and get their response?