Not that bad.... no need to be too alarmist.
I let my 16 yo son use Snapchat, but would certainly not let my 10 yo daughter (and will probably keep her off it until she is 15 depending on her maturity).
Snapchat gets a bad rap since all messages disappear quickly. As a result, kids can send something mischievous and not get caught. And parents can't keep up with their kids' messages in the way they can with texts. So the parent bandwagon has been to require one of two things: either make your kid befriend you on Snapchat so you see what he/she is posting or make your kid delete the Snapchat app altogether. But I say neither is the answer. First of all: there are some good features to Snapchat. This article here (google - Huffington Post What Parents Don't Get About Snapchat) outlines that well. Secondly, keep in mind that anyone can create more than one Snapchat identity. So while you think you're following you kid on Snapchat, he/she could have an entirely different identity you don't know and aren't following. So don't waste your time with that.
Its also important to know the culture of teen messaging (texting, PMing, Snapchatting, etc). There is a lot of bravado that is done on message sites that is not necessarily representative of the kids' reality. They like to show off online by saying things they'd never really do. Digital media offers a sort of anonymity or a sense of being a step or two removed from reality. As a result, kids will talk about all kinds of things to sound cool, when in reality they'd never really do any of it at all. So you can drive yourself nuts trying to decipher things or figuring out the what/why/how of their messages, only to eventually determine none of that is going on at all. I've been there. I'm a counselor myself and have consulted with child psychologists as well. And I've concluded its just not worth it to comb my son's messages. So I don't do it anymore. I would say this - if you think your kid is really at risk (getting bad grades, hanging out with the wrong kind of kids, sneaking out at night, etc), then sure read messages (but take everything with a grain of salt). But if your kid is doing ok (decent grades, responsible friends, etc), then forgo the message reading and don't be alarmist about Snapchat. Most kids make mistakes and aren't perfect (and I have been through my share of challenges with my son), but unless you are really concerned, then let your kid have some privacy. If a kid feels too watched (even the good ones), he/she can respond by upping the ante and being even more sneaky (which is not want you want). But if you have open conversations and set appropriate limits, know your kids friends, and see good grades and reasonable decisions happening, then give your kid some latitude and you'll probably have few issues than if you are very protective. And I don't say this as a lax mom at all (I'm fairly watchful and my son thinks I'm "strict"), but I've also learned how to not drive myself crazy either. Just some things to think about when it comes to messaging apps. Of course, each parent has to make his/her own decision based on the family and kids involved.