Jeju-Do in November/December for kids?

Hi,

We are planning a trip to Korea end of this year with our 2 kids (age 6 1/2 and 3 1/2 years). Not sure of dates but may be around November and December. Just wonder if that is a good time to visit Jeju island with little kids? Is it going to be very cold and is transport to get to and from Jeju island to Seoul going to be easy?

We are thinking to stay a few days on Jeju island so hoping someone can point us to some sites on things to do when travelling with young children at that time of the year.

Thanks!