Is neccessary to store christmas cookies in the fridge?

Butter biscuits (cookies) and gingerbread both keep well for days at room temperature in an airtight container. Some gingerbread will keep for much longer. For most cookie recipes it's a matter of the quality spoiling rather than food safety. Pastry and biscuits tend to spoil by going soft absorbing water from the air, so they really do need to be sealed up.

Don't forget that the keeping properties of the finished product will be different from those of the base ingredients. So have a look at the recipe. A decent recipe book should have storage instructions for the recipes; if it's a family recipe and you don't have this information it might be worth consulting a similar recipe online or in a book. In addition it's a bad idea to keep soft biscuits (like some gingerbread) in the same tin as crisp biscuits (like shortbread or butter biscuits) as the crisp ones will soften and the soft ones dry out. So you might want to keep each type in its own container.