Generaly speaking, venomous snakes have slit pupils and non venomous have round pupils. It looks like there are only four common venomous snakes in TN.
http://frogsandsnakes.homestead.com/snakes.html
Couldn't readily find anything on the spiders commonly found in TN, but there are really only 6-7 hazard species of spiders found in the states, so if you learn those, you should be reasonably safe.
http://www.rochedalss.eq.edu.au/spider/spider1.htm
Spiders are very helpful little beasties, so if you're finding them outside, it's probably best to just tip your hat to them and move along.