On the 10th, snow will fall throughout the day and on the 11th, you should find that your grass is covered in the stuff. Apparently the snow flurries were possible from the 26th November onwards, but I've only had one happen in the City so far. There's still time for the snow flurries to fall before the 10th though.
Fire Fist is correct, i've just been to Let's Go to The Wiki and it says that, if your lucky, you can get your snow flurries early on the 26th of November, same, i've had them in the city, yay! 10th of December is when my internet downloads come back and my computer will be fast again!
I agree with Fire_Fist and Mariorock09. On December 9, you get a message on the bulletin board in front of town hall saying, "We should be expecting a snowstorm tomorrow. Bundle up!" Or something like that. On the 10th, the storm comes. On the 11th, you will see the snow covering the ground from the previous day. Hope I helped! :]