sensitive skin and clothing

Hi ladies,

I'm going to have a winter baby , and I am looking for a good quality overall/coat to keep him warm through the winter when we go out. However, I was wondering if fleece lining were ok for babies with potentially sensitive skin / eczema prone ? We have a history of sensitive skin. Any mommies out there in the same situation?

Almost all the overalls have fleece in them and sometimes faux fur decorated hoods.