Answer A is perfectly grammatical. The problem with these multiple choice questions is that they often are asking multiple things at the same time, some of which have nothing to do with language.
As you say, "consequently" usually means "because of that;" consequently, if you chose answer A, you'd be saying, "We decided to go mountain climbing because it was cold." The question writer expected you to assume that people do not like to go mountain climbing when it's cold, or that they wouldn't choose to go climbing specifically because it was cold. They probably expected you to think mountain climbing happens outside and people like to be outside when it's warm - therefore, people like to go mountain climbing when it's warm, not when it's cold. However, there are types of mountain climbing (like ice-climbing) where the threat of melting snow and ice makes the climb much more dangerous. In this context, it would make perfect sense to say "We decided to go climbing because it was cold."