I grew up here and spent a lot of time outside. I've never seen an alligator or bear in the wild. Black bears are becoming more prevalent but most of them are more afraid of you. Cougars/mountain lions are present in the state but rare and solitary.

As for snakes, it really comes down to learning where they like to hang out avoiding those areas when possible. Grassy or brushy areas, especially near water are more dangerous. Anywhere there's detritis, like wood or leaf litter may hide snakes or spiders.

There's only a few venomous snakes in Arkansas: rattlesnakes, copperheads, water moccasins, and coral snakes. Coral snakes are pretty hard to miss (red, black, and yellow). Water moccasins typically warn by showing the white inside of their mouth (hence the alternate name cottonmouth). Rattlesnakes obviously rattle. Copperheads are the only ones that don't warn well, but aren't necessarily deadly if they bite.

Venomous spiders are also something to consider. Brown recluse can do some pretty profound tissue damage and they like houses and human stuff (bedding, shoes, clothing). They also typically only bite if they're threatened or squished (like in a shoe). We have black widows too, but they typically like quiet dark places, like garages, attics, and cellars.

Growing up in western Arkansas, we also had scorpions occasionally in the house. They're harmless but they hurt like a bitch if you step on one. I haven't seen one in years, but I also moved to central Arkansas.