ummm no, but it is a handgun, which would be allowed to be carried while hunting and OP original question was if hunting was allowed in the area, and the answer is yes-
is allowed in the area, on private property- (and other places) with varying degrees of licensing and permitting and regulations around days, dates, times and bag limits -
I don’t think the S & W is a small game weapon (or at least not a practical normative one-)
I was speaking to hunting in the area and the right to carry handguns while hunting