I know it's not the best bike out there, please no criticism. I am not looking to spend a whole lot and this looks like a pretty decent bike. I just have a couple questions about it. First of all, this is the bike...

26" Schwinn Sidewinder Men's Mountain Bike, Matte Black/Green - Walmart.com

I am buying this same bike off from a guy on craigslist for 60 dollars, he said it is in like-new condition, nothing wrong with it. My main question is though, if I for some reason don't like the design of the handlebars, how hard is it to replace them with different ones, and is it even possible?

Yeah, you can put any handlebars with a 25.4mm clamp diameter in there. Big cruiser bars might require you to get longer cables and housing, though.