gloves on shabbos

Question

The Shulchan Aruch brings down a person should not wear gloves on shabbos,because he might take them off to shake someone hand and start to carry them. The Bach says it is ok to wear gloves on shabbos. According Shulchan Aruch in a real cold day when a person will not even stop to greet someone,because it's so cold, he would matir it.Or just be somach on the bach.Or neither don't wear gloves.