On a warm enough winter day you might sneak in some climbs at Cedar Point in Saint John, a sport crag on quarried limestone. Cochrane Lane cliffs in Welsford is the major destination but has limited sport climbs available. The Gollum's Cave area is usually the driest. You might also find sunshine, dry stone, and sport routes at Sunnyside in Welsford. Sunnyside might be harder to follow a trail in winter.
You can get a copy of the guidebook at Scout Shop in Saint John or Radical Edge in Fredericton. There is also info online at Mountain Project and
http://www.beta-source.comGood luck.