Ice climbing - December through March. Most of the time you will be driving to Lillooet which is 5 hrs from Vancover, for a weekend of ice. During prolonged cold snaps (usually once a winter for 3 days but once every 5 or 10 years last for up to a month) there is accessible ice within 30 minutes of Vancouver.
You can rock climb in Squamish every month of the year. However, in November through January, that might be one day a month. There are always sunny weekends in February, March, April and May. June can be pretty damn wet but July through September are usually sunny and hot. Monsoon begins again mid to late October.
For alpine climbing, if you are lucky you can bag two technical peaks per winter. The number is much higher for ski-ups. Alpine climbing in the spring features great neve and mixed and best of all, the bush is covered by snow. Alpine rock season starts in May and lasts to early-mid October.
It is not unreasonable to climb 100 to 120 days per year without ever leaving southwest BC. If you are like most people though, you will take advantage of climatic disparities to head down to Smith Rocks for sunny rock in November or March, or over to da Rockies for fat water ice in early December when local creeks aren't even frozen.