As everyone else mentions, Venus Flytraps typically grow more prostrate (flat) and hug the ground during cold weather to help keep them warmer (from freezing). The plants usually begin to grow shorter, more horizontal leaves a month or two before dormancy, and the leaves remain that way throughout dormancy and usually for at least a few weeks after dormancy when the plant begins to grow actively again.
In most Venus Flytraps, the leaves begin to grow thinner and more upright as the weather becomes warmer, but some Flytraps have ground-hugging leaves all year.
During dormancy, try to prevent the leaves from freezing, so that they can still produce food for the plant from photosynthesis. Cool to cold but not freezing temperatures are great. Give the plant plenty of light even during dormancy, and don't water nearly as often because the plant uses much less water during dormancy and the growing medium dries out much more slowly when it is cool or cold. You can allow the medium to dry until just barely moist before watering again, unless the plant looks like it is drying out completely.
Best wishes, good luck with your Venus Flytrap, and please post messages to the Forum about its progress and your experience.