French, living in UK, I've been going to Cogne for 20 years. It's been fabulous for lots of reasons.
It's first and foremost an all-rounder resort. Perfect for families with younger children that want diverse activities, some luxury and traditions. The villages are really authentic and because of it being in the Gran Paradiso national Park, nothing ugly ever gets built. You have a smallish downhill ski area with 700m vertical and a huge cross country one that is very picturesque and hilly, and goes in several different valleys allowing for constant change of scenery, including to the foot of the GranParadiso glaciers.
If you're after ski only and miles of lift-served pristine snow, then you must go elsewhere. The skiing area is limited by the fact it is within the National Park. But the 3 lifts of the main area serve a limited number of north-facing tree lined red pistes of top quality. It's steep and spectacular. And not for beginners.
The good thing with small resorts is the friendliness of people, the value for money, and the very human size domain that allowed our small children to be left on their own very quickly. You cannot get lost, always come back to the same point and there are only two very friendly bars and one restaurant on the pistes. That's it. Once you've done your day on half day, there's always something else to do. Spas, hikes in remote valleys with fabulous frozen waterfalls like in Lillaz, tobogganing...and enjoying the superb restaurant scene.
It's remote, but big enough to have everything. If you're lucky you'll see Ibex and Chamois by the pistes.
It's worth hiking up the Grauson from Gimillan for the most spectacular views of the Gran Paradiso group. Also do not miss the waterfalls in Lillaz and Valeille and the flat but beautiful walk towards Gran Paradiso in Valnontey. Cretaz is another authentic mountain village.
We spent many full weeks there, always sprinkling our Cogne skiing days with excursions to perfect La Thuile, or Pila (40mins away, a bit too crowded in our opinion, but Chamolé piste is one of the best in the region and in good conditions the safe offpiste is great). We will try Crevacol this Xmas as the Powerhounds reviews are so good! Cervinia is not too far for a day either.
All in all a week in Cogne is a great round-up winter wonderland holiday. It's only beaten by going there in summer: unspoilt, wild, empty stupendous scenery...but that's for another crowd!
Enjoy!

Pros: authenticity, remoteness, 4000m mountains and glaciers scenery, variety of easy access activities, quality of accommodation and restaurants, empty pistes, value for money, quality of ski, snow playground and baby piste in the village, easy spectacular walks away from any roads etc. A lift weekly ticket at Cogne gives you a couple days skiing in Pila. The tourist office is very efficient and proactive. Excellent shuttle service between Aosta train station and Cogne, and then to the other villages of the valley. Ski school with little numbers

Cons: limited ski area, limited downhill ski rental options, no parking by the gondola, you'll have to walk up through the village or park by the meadow at the bottom.
See our video here