We spent last Thanksgiving there, and were told the RC closes from the Monday after Thanksgiving until after the Christmas break, since the hotel is very slow that time of year. The weather is very nice during this time period, so I would think it is a great time to visit Palm Springs.
The RC club being closed is no big deal, since it is one of the least interesting of the Resort RCs. They charge for drinks, and it is obvious that when they built the hotel it was not designed to have a RC, since it consists of tables and chairs set up in a hallway.