Mei strength comes from her ability to freeze one of her opponents. To do so, she has to use her freezing ray a few second on an enemy at a relatively close distance.
If you analyze my first two sentences you can guess what are Mei's weaknesses:
freeze ONE of her opponents
By grouping with your allies, it won't be easy for Mei to freeze you and shoot an icicle through your skull. Moreover, if she is alone against your team and use ice block, you should get plenty of time to decide to flee of finish her!
use her freezing ray A FEW SECONDS
Mei doesn't have the biggest dps of all the Overwatch characters, as I said earlier, she rely on her crowd control more than on her damages. This means that if you out damage her in two seconds, you win. Roadhogg is a good choice, but while playing this guy you are more likely to play close to your team mates, meaning a good Mei should not be here (Mei is probably killing your lone mates).
My favorite character to kill Mei (and my favorite character overall) is Reaper. Once you get close to someone you can deal a ton of damages really fast. If you are really good, you can kill her in two shots (she probably won't have time to use her ice block). Moreover, if things turn bad, you can still use your Shift ability to flee, remove the slow effect of Mei's gun and reset the freezing process.
a relatively CLOSE distance
If Mei can't freeze you she will have an hard time to kill you. Stay far away from her and use your mobility to flee/chase her. A good Widowmaker/Hanzo can snipe her or flee easily by climbing walls.
Finally, don't forget that taking your opponents by surprise, knowing your enemies, knowing your character and knowing maps will help you to be a better player.