Is visiting Europe in January-Feb a good idea?

We're going there this coming middle Jan-middle Feb. I know it's winter, of course it could get cold and snowy. But can it hinder the vacation? Like are some tourist spots closed or most of the time we will just be indoors? Were visiting Paris, Barcelona,Madrid, Bern and Rome, by the way. Can we still visit the Eiffel or will it be very snowy? I wish some locals or those who have been there during winter can shed some light. What can we expect on the vacation due to the weather? Is it better to go during March? Thanks