Most wine ingredient kit instructions tell you to ferment your wine within a specific temperature range. Midwest recommends 65 °F to 75 °F. Yeast thrives at these temperatures, and also likes to be kept at the same temperature until its done doing its work. If the fermentation area is too cool, the wine will ferment very slowly. This will lead to an excess of CO2 gas in the wine, and it may not be ready to stabilize and fine in the expected time frame.
Additionally, the fining agents included with wine recipe kits don’t work well at temperatures outside of the 65 °F to 75 °F range. Below 64 °F your wine kit may not clear at all! Since most people keep their house at around 68 °F, just leaving your fermenter at room temperature should work out great.