Is neccessary to store christmas cookies in the fridge? If I want to have a Christmas cookies e.g. in a different room than the fridge is, how long I can leave them at room temperature without worry that it will be spoiled?

This types of cookies mostly contain butter (not good for leaving outside of a fridge) but also alcohol and sugar (good for leaving outside of a fridge).

I have for example this types:


Shortcrust pastry (first picture)
Wasp nest (maybe known only in my country I am not sure, see the second picture)
Gingerbread
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.