Can my Zebra Finches breed in the winter?

I have had my finches for well over a year, i now have about 10 breeding pairs and have had over 20 chicks from them this summer. Last winter they laid eggs but i decided to remove them because i didn't know if i could let them breed in the winter. Is it best to let them have a break and remove all the eggs they lay or should i let them breed? im just worried that the chicks will die because of the cold... any answers appreciated. I live in the UK last winter was cold and i think its going to be another cold winter.