Guest,
My guess is that you have a Winchester rifle in .32 Win Special caliber. But that caliber was made in several different Model rifles. I would like to know which model rifle you have.
Special order checkering patterns could be had from Winchester and Hunting scenes engraved on the receiver were also available. Both at extra cost. I have never seen hunting scenes "carved" in the wood. The relative softness of the wood would cause them to not have much detail and they would be more easily worn and damaged. My guess is that the carving was done aftermarket. I have seen several examples of sort. Most are rather simply done.
I would love to see some photos of yours. The photo below is of work done the master engraver John Ulrich who worked for Winchester in the 1880's.
Thanks
2bit