At Hindu temples in places that get really cold (e.g. New York City or London), do people have to go barefoot outside on the temple grounds? I know many temples in the United States are all indoors. But some (such as the BAPS temples) have extensive grounds outside. (And an article on BAPS Shri Swaminarayan Mandir in London mentioned "barefoot women in saris going up the stone steps"--is that only when it's warm out?)
According to words by elders and holy books, temples are one of the places where footwear is not at all allowed. We should not go to a temple wearing footwear. It is a rule. So, this rule applies everywhere in the world and not only in India. But people follow it for several reasons. Some follow it as a custom. Removing footwear indicates respect towards the purity of the temple. Some do not carry footwear into their houses too. This is due to customs or cleanliness reasons. There are some other reasons too. For more detail, See Why do Hindus remove their footwear before entering temples?
To answer the question particularly, the scripture also gives some exceptions while following rules. It doesn't force you to follow an injunction at any cost. E.g a person is given some alternative when he can't bath perform or perform a daily ritual in an emergency. This are given when a person is not in a position to perform an activity due to ill health or a natural calamity. (Source: a YouTube video of Chaganti Koteshwara Rao about types of bath and its exceptions.) So, the same rule applies in your case also. When there are cold climatic conditions like snow fall or heavy rain fall and you can't remove footwear very distant from the temple, you can remove them some place nearer. Temple management also makes some arrangements to leave footwear so that there would be no problem to the devotees. Generally, there are footwear racks to keep your footwear. You may leave them and walk barefoot from there. You should wash your feet saying some maarjana mantras or at least say "Pundareekaksha Pundareekaksha Pundareekaksha" an sprinkle water on your head.