In NYC, we are out on the streets, exposed to the elements, as we walk from the subway or bus stop to our shopping destination, and again, as we wait in the cold air on icy sidewalks for the train or bus to the next destination. So no, when the temp is in the teens fahrenheit, I generally avoid shopping.
When I first started shopping fifteen-plus years ago, the purpose for shopping was different so companies had a rule: Avoid shopping on bad weather days. We were given a range of days to complete shops.
The reason for avoiding bad weather shops was that the store or restaurant employees were likely to be in minor fender bender accidents or stuck in snow canyons; if they then show up late, they are likely to be error prone and anxious during the time you might see them. Also, the regular employees might not have been able to leave home, and the substitutes might have been called to work at the last minute, leaving them error prone as well. It may only be the manager who can make it to a boutique to open it, and that person may have to deal with 10 customers , nine of which entered the shop just to keep warm. Whatever the case, shopping in these conditions was likely to result in a negative shop result.