This started in Denmark in the 1970s, although even before that it was common to take a pair of slippers or a pair of shoes with you when you went to visit someone in the winter, so you were not marking their wooden floors with wet boots.
Or for that matter sitting indoors in boots and thick socks necessary outside in the winter cold.
Now, it has become common to take shoes off in the hall.
We always did so if we were wearing wooden clogs, so did the Dutch, and I believe in Austria and Switerzerland it was unheard of not to change shoes on coming indoors.
It is definitely a cultural thing. In Italy, Spain and Portugal where most floors are made of tiles, you didn't do this.
If the floors are cold in a house where you are expected to leavee your shoes at the door, take a pair of thick socks with you to put on. Your host is unlikely to object to that. You could also ask if you might bring slippers with you.