Jargon for Snow Sports

alpine - Relating to high mountains, especially high up above the treeline. This treeless region is a nice place to make big, fast turns without worrying about hitting a tree. It is more susceptible to bad weather, which is essentially why there are no trees there. The environment is too harsh there for them to grow.
alpine touring (AT) bindings - Ski bindings for backcountry skiing. For skinning uphill, the heel detaches, and the toe portion hinges, allowing a walking motion. They function like regular downhill bindings when skiing downhill.
alpine touring (AT) boots - Ski boots designed for backcountry skiing that have a "walk mode" enabling the boot to flex forward more freely. They are also lighter and somewhat less stiff (in ski mode) than regular alpine downhill ski boots. They are occasionally used for backcountry snowboarding.
backcountry - The backcountry, in the skiing/snowboarding sense, is any area outside of a resorts boundaries. There are, however, limits. As discussed in out of bounds riders are prohibited from entering some areas outside of resort boundaries due to the possible endangerment of the rider themself, or others. Examples include cliff areas, or areas where a triggered avalanche may run back inside resort boundaries. The backcountry should only be entered if you have the proper skills (avalanche training, etc) and gear (avalanche equipment, clothing, etc).
backcountry skiing or snowboarding - Skiing or snowboarding done in the backcountry, outside of a ski resort. Also known as touring.
booting/bootpack - The act of walking uphill in ski or snowboard boots to access more/higher terrain. This is usually on a steep enough slope that a steps form in the snow, and subsequent people use these snow steps to climb. The snow steps that form are called a bootpack.
cirque - A steep bowl formed by glacial erosion, usually containing cliffs and chutes.
couloir/chute - A steep, narrow gully lined by rocks on either side. They can be used interchangeably to some extent, although chutes are typically smaller, where couloirs are longer.
crevasse - A deep, open crack that forms in a glacier as it flows downhill. These present a significant hazard to backcountry travellers in glaciated areas.
flat light - A visibility condition where light from the sun is mainly diffused instead of direct. This reduces shadows, and this makes it difficult or impossible to discern texture on the snow surface.
glades - A ski slope that is sparsely treed. Within ski resorts, they are usually rated as a blue or black diamond run. Often the trees have been manually thinned out by mountain operations in order to increase the ski area. If there has been no recent snowfall they usually have moguls.
glacier - A slow moving mass of ice. In areas that are cold and/or snowy enough, snow from the winter doesn't completely melt in the summer. As a result, over many years, even centuries, snow continues to accumulate. The weight of the accumulated snow compresses the underlying snow into ice. Gravity causes this ice to flow very slowly downhill.
groomer - See piste. This term is also often used for the snowcats that do the grooming.
gully - Like a large ditch, that has been eroded by a creek or stream. Gullies can collect snow meaning they are fun to ski in, but they can also lead you down creekbeds where you may get stuck or lost, so be wary!
moguls - Bumps in the snow that form due to skiers and snowboarders moving the snow around the slope as they turn*. Typically 1-3 metres across, and 0.5-1.5m tall. *In mogul competitions moguls are usually made by snowcats, they are larger and more regular.
off-piste - Any ski run within a ski resort that is not groomed or prepared as a piste, but left as a natural ski slope.
out of bounds - Ski resorts mark their boundaries with ropes and signage. The areas just outside of this that is usually closed to skiing is known as "out of bounds". Rules vary with resort, weather, timing, etc. Skiers are sometimes prohibited from going out of bounds. Sometimes they're permitted. Sometimes it's permitted only after getting permission from the resort. Sometimes it's permitted in certain areas e.g., a backcountry gate, but not in others e.g., areas where a skier may trigger an avalanche that runs back into the ski resort. It's very important to inquire at the resort base or a ski patrol shack about the rules, or pay very close attention to signage. You could be putting your life and the lives of others at risk.
piste - A groomed and compacted ski run.
splitboard - A snowboard designed for backcountry use that can be taken apart to form two "skis" for skinning uphill.
skinning/to skin - Hiking uphill in the snow to reach more/higher terrain with skis or a splitboard on your feet, and skins on the bottom of them.
skins - Synthetic animal skins (actual animal skins used to be used but not anymore) that have synthetic hair on one side and glue on the other. The glue side temporarily sticks to the bottom of your skis/splitboard. The synthetic hair allows you to glide in the forward direction, but prevents you from sliding backwards, enabling you to walk, or skin, uphill.
snowcat - A large grooming machine with tools attached to it that churn, till, and then compact the top 10-15 cm of the snowpack as it drives slowly along. It has tank-like treads allowing it to drive on snow.
telemarking - A skiing technique originating in the Telemark region of Norway, that combines Alpine (downhill) and Nordic style. It is still practiced by some. Only the forefoot is attached to the ski, and the heel is retained in the binding by a tensioned-spring. Telemark skiers use telemark-specific boots and bindings.
tour/touring - A term interchangeably used with backcountry skiing or snowboarding. A tour would be a backcountry skiing/snowboarding trip.
traverse - A one-way backcountry trip that covers a large horizontal distance. Many traverses cover extensively glaciated areas (ice sheets). It can also mean to travel laterally across a mountain, usually without losing or gaining any elevation (i.e. travelling to an area where you want to then make some downhill turns).
whiteout - Fog that is so dense that it is difficult or impossible to see anything around you, sometimes even your feet. A whiteout makes navigation, and even skiing, virtually impossible.

A great glossary for avalanche jargon is hosted by the US Forest Service National Avalanche Center.