As said, they are aggressively into making snow, but it's not that there's no natural one. If you like to ski marked trails and leave it at that, you'll have plenty itineraries. Buy the Dolomiti Superski skipass, it will give you access to all the valleys of the consortium.
A classic off-piste route is the Val Mezdì in the Sella group. Go see the guides in Corvara, their offices are near the ice stadium IIRC, or at Sport Kostner. Ask for " Enrico" (if he's still there), not a chatty guy by far, but very competent, have your own AVI gear, jic.
The day will involve you skiing half of the Sella Ronda trails till Passo Pordoi above Canazei, take the tram, maybe ski the Forcella del Sass Pordoi if the guide will think you'll be able to do it and the weather and time schedule will allow for it. Rest and eat something, then hike 30-45 minutes (on nearly flat ground, I say nearly, not completely) till the vallet mouth, then ski down to reach Colfosco, and from there take the lifts/trails back to Corvara.
If staying on marked trails, beside-the-trails off-piste is generally "implicitly" allowed, but beware of the "humour" of any policeman you'll be likely to meet. Observe if the sides are already skied or not, read the signs. On October 7th, 2009, two Swiss citizen have been found guilty of charges and sentenced to two years in prison for triggering a small avalanche in the Dolomites sidecountry in 2004...So, be careful and if you don't know the place, don't do.
Another nice ski trip involves boarding the bus in Corvara or Colfosco or La Villa (one could go skis on foot, but then will have to fight to board the bus in Armentarola, being the latest point where one can arrive skis on foot on that path, the bus station is tipically stormed by people and believe me, even regular european queues are better than that) and reach the Passo Falzarego,just above Cortina, ski there a couple of runs, and then ski back down till Armentarola using a marked ski route/run. Typical is also, once reached the bottom of the run, either ski in the flat river bed (extensive use of poles to push is required) or to pay and be pulled by a horse to Armentarola (don't stay right behind the Horse though)
A place to ski is the Marmolada mountain, but be warned, there are three tram stratches and to reach the top will be quite lenghty. Also a very cold place. Here the trams could be very crowded. IF you have time, visit the WWI museum...
Christmas week will be very crowded, and in the past years Corvara has become a "Posh" spot for celebrities to go, adding itself to the likes of Cortina and Madonna di Campiglio. If you don't have already a room, look for places in Colfosco, the just up the valley village.
Or at La Villa ("La Ila" in Ladin and "Stern" in German). The "Gran Risa" (that's the official name of the Alta Badia GS race track) is surely to be skied, but try to ski it early in the morning before all the "cannibals" will go and ski it.
Another I like is to take the lifts till Passo Gardena, ski down to Selva (take the Dantercepis run on the skiers' right, if open, it's another DH race course, used for the military national championships), then go to the Sasslong, ski down to Santa Cristina, take the underground tram, ski the Seceda, and reach Ortisei, then ski back.
Selva di Valgardena is home to the Carabinieri, Moena to the Police, Predazzo to the Guardia di Finanza police, mountain divisions, btw.
Carabinieri are usually dressed in dark blue/black with a thin red stripe. National Police blue/gray with a red/pink stripe on their uniforms and usually the word "Carabinieri" or "Polizia" written on their shoulders. Corvara hosts a small mountain troops camp so youìll also see
Alpini to ski around in their gray/green 8or camo) uniforms
If Saslong A and Gran Risa (both black runs) will be closed because of the WC events, then try the alternate ones (both red ones), the Saslong B, very scenic, "passing" by a middle age castle on its way down to Santa Cristina. And the alternate to Gran Risa (never manage to remember its name, it's trail number 17 on the Alta Badia map you'll find at the site I point you to at the bottom here)
Gran Risa has become easy, IMHO, compared to some years ago, flattened, widened, a small off-piste variant closed, and given its name and fame derived from the WC, every one wants to ski it...
From any of the villages you can move skis on foot throughout the valleys, by use of a combo of the lifts system, runs and regular transportation...
Beware, in your wanderings, to take into account the lifts closing time or you'll end up paying a taxi to be shuttled back "home" (it happened more than once to me...)
Season is scheduled to pre-open on Nov 21st or at the latest on 28th there, with the traditional first crowded date being Dec 7th/8th (long week end in Italy) let's see how the snow is going to fall. Keep an eye on webcams.
Sceneries are breathtaking, be sureto be on some "peak" at dusk to enjoy the "Enrosadira" (all Dolomites as far as the eyes can stretch are assuming a pink/red colour).
As said the place will be crowded, once upon a time the "mainstream" tourists were Germans/Austrians with Italians being a "tolerated" (despite the region belonging to Italy since 1918, WWI scars are still present and feelings on the part of the German speaking population are still there, under the surface) third group. Nowadays the place is likely swamped by Ru$$ians and other €ast€rn €urop€ans. But I've also met and skied with Americans and northern europeans (Belgians & Dutchs)
More infos at :
http://www.dolomitisuperski.com/Edited by Nobody - 10/9/09 at 5:45am