It's a thing and I was going to say if you live Central London, Brighton, Bristol, somewhere with an eclectic mix of people, fashion wise, then go for it. I would. (I'd say go for it if you like it regardless, but seeing as you're asking in S&B, you're obviously unsure)
Not sure about white for winter though. I'd have thought brown or black with a grey or fairisle sock, faded jeans and chunky sweater would look good. (Pinterest has loads of looks if you search Brikenstock sock outfit!). I also like the slip on Boston with socks too, although that's probably more acceptable.