Hi nico6196.
I am glad that you posted that question,because I also have little seedling identified as Barberry Bush.I am not sure how to protect it against winter cold.Thick layer of mulch and protection against winter wind by covering the plant with burlap.this is what I would do,but maybe there is some better way to help the plant to survive.
Hala

{{gwi:540756}}

Here is a photo of mine.can you see similarity?

Barberries are hardy to zones 4 and 5 based upon the kind you have, but I would simply mulch the seedlings a bit and leave them be. At my former house I used to have a hedge of them and many times found seedlings at their base. I never did anything to protect them as this shrub was not considered garden worthy in the mid-80s. Now I could make a mint selling them!! LOL!