Your biggest danger will be getting lost in deteriorating weather.

I'd look into when the bears come out of hibernation and when they have their cubs, and follow the precautions for that. I wouldn't let it keep me out of the woods. I don't remember ever hearing of someone being killed by a bear in the state.

If you get lucky enough to see a cougar in the wild, I will envy you. Those things are so elusive you have to hunt them with dogs wearing radio collars.

You maybe might see a rattlesnake? It's pretty rare to get bitten by one.

ETA: During deer season, while not required to unless you're hunting but still a good idea, wear a hunter orange vest, or one of those bright green ones like road crew guys wear. You'd hate to be mistaken for a deer.

To mitigate your risk, let someone know where you will be in general, what you will be doing, and when you expect to return. Carry something like a space blanket and wear a hat in case you get caught out overnight. Stuff like that, there's a million youtubes about things to put in a daypack.

Other than that, enjoy your walk.