Read here. The ozone hole is "believed" to have a major impact on the climate, especially in the Antarctic region. It is hypothesized that more ozone destroying CFC's in the atmosphere causes warming, but in the Antarctic area, the decreased ozone due to CFC's causes cooling. When the ozone hole closes, as a result of less CFC's, this supposedly will cause more warming in Antarctica. Unfortunately, this science speculation is more than just a bit fuzzy, and as a result, the climate models are rather schizophrenic on the critical ozone impact on the global climate.
"The projections from the measured data does not provide a clear picture of how fast the changes will take place or how significant they will be. In their prediction of future climate, many IPCC models did not consider the expected ozone recovery and its potential impacts on climate change.....which may have profound impacts on the surface winds and on other aspects of the Earth's climate, including surface temperatures, locations of storm tracks, extent of dry zones, amount of sea ice, and ocean circulation.....“Our results suggest that stratospheric ozone is important for the Southern Hemisphere climate change, and ought to be more carefully considered in the next set of IPCC model integrations,” said lead-author of the study.....Meaning that the current IPCC models, the ones that all the global warming predictions are based on, are not correct."
As an aside, how much smaller is the ozone hole since enforcement of the Montreal Protocol began in 1989? Unfortunately, after 20 years the ozone hole size still exhibits an upward trend in growth and the maximum size remains well above the 1989 hole size. Additionally, its wide annual size variation suggests an impact factor other than simple human CFC's at work. (click on image to enlarge)