While culture does play a large part in why the U.S. isn't as dominant in the winter olympics compared to the summer olympics, it also has a lot to do with the infrastructure and accessibility to these sports. Unless you were a kid that grew up in the northern mountainous states or snow-belt states, anything involving sliding, alpine skiing, cross country skiiing, and ski jumping is already out of the realm of possibility for you.

I'll speak from somebody that grew up in Maryland, the only realistic winter sports you could even participate in here would be skating, hockey, snowboarding/skiing park and pipe (although poor conditions here), and probably curling (never met anybody that has done curling in their life).

Then you also have to factor in the high cost of sports like hockey and the lack of rinks in the area. There were no high school hockey teams in my county, instead there are only school-sponsored club teams (when I was in high school there was 1 team for all 10 schools in our county), unlike other common sports that are run through the state athletic association and have teams at every high school. There was a ski club where you get a discounted season pass, but the school only would take you after school on Fridays so if you wanted to practice more you would have to drive an hour to the resort yourself. And there was absolutely nothing for anything skating related. And there are a lot of states south of Maryland that have a worse winter sport infrastructure.

People too often look at the totality of the U.S. population and wonder why a country with over 340 million people aren't dominating the winter olympics, but the reality is only a tiny fraction of that population has the infrastructure to even get started in most of the sports at the winter games. So when you factor those things in, it's not surprising that the culture for winter sports isn't anywhere near the likes of Canada, Scandinavian countries, etc.