It's not cold as you think. The highest point there is about 500 meters, so it might be a little colder than on the downtown area, but not that cold.
For places to have lunch, there is MacDonald, Bubba Gump Shrimp restaurant and the Victoria Peak Restaurant.
From Causeway bay to peak, you may take MTR at causeway Bay station to Admiralty Station and then take Bus 15 to the Peak; you may also get off at Central Station and take cable to the peak.