If you walk into a Telemark ski store, for example, you will find lots of options for different kinds of skiing. There is downhill skiing, competitive skiing, and cross-country skiing. To keep things brief, the following just discusses cross-country versus downhill skiing differences, equipment, and places to go for each.
For the most part, you are mushing through the flat country on skis. Trails dedicated to cross-country skiing are designated on state and federal park maps. You can only cross-country ski in winter and when there is enough packed snow for you to stay on top of it as you slide one foot forward at a time. The poles tend to be longer than downhill ski poles because they are used to help propel you forward so that your feet on the skis just glide. The best places to ski are the northernmost parts of the U.S. in winter and Canada, where cross-country skiing is only second to snowmobiling as an outdoor winter recreational sport.
Downhill skiing is what everyone thinks of when skiing is mentioned in general. Skis for downhill are longer in order to support your weight as you gain speed going down a slope. There are many skill levels for this sport, and you have to practice on hills that are gradually harder and harder to maneuver. It is particularly more dangerous than cross-country skiing because you gain a lot of downward momentum skiing down a mountain slope. There is also the dangers of hitting trees, boulders, and the potential for snow slides and avalanches.
The good news is that you do not have to wait for winter to ski downhill. There are many ski resorts in the U.S. that are open almost all year round. Some of those resorts can be found in Colorado, California, and upper New York State.
Other Pieces of Equipment You Need
Protective sun/windshields for your eyes and face are highly recommended for downhill skiing. Appropriate winter attire (e.g., snow pants, waterproof winter coat, mittens or gloves, and a hat) is required to protect your body, skin, and keep you warm. Unless you tuck scarves into your coat, they are definitely not recommended for skiing as the tails of a scarf can get caught on branches, bushes, etc., and pull you off your balance while on your skis. Ask your skiing store associate what he/she would recommend for gear.