We are planning on going at the beginning of December. Would there be snow there?

Early December snow is unlikely but certainly possible.

Yes

Always be prepared for snow! Carry chains (not cables!) because you will not be allowed up here without them and know how to put them on.

Most snow tends to fall after the first of the year, but it has been known to happen!

Most likely. I'd make sure to check the weather, and plan accordingly. Ie Snow jackets, snow chains..