Part of the astonishing variety of the French Riviera landscape is the fact that while standing on the beach, enjoying the warm water of the Mediterranean Sea, you can see the snow-capped peaks of the Southern French Alps.
In spring, you can easily ski in the morning, and enjoy the beach in the afternoon.
The French Alps extend all the way down to the sea in the eastern part of the Riviera. The highest peaks in the Southern French Alps are Mont Capelet (2935m) and Mont Bego (2872m). Just across the border with Italy there's a couple of peaks exceeding 3000 meters.
There are a total of 15 ski and wintersport resorts in the Alpes-Maritimes (note the Cote d'Azur runs along the coast line of both the Alpes-Maritimes and Var departements), all within one or two hours drive from Nice.
The skiing season runs from early December until late April. If you can, avoid the school holidays, because the resorts get very busy during those periods (see also practical info.
All of those resorts are definitely worth a visit in other seasons too.
The most popular, and closes to Nice, is the resort of Isola 2000. It takes about 1 hour and a half to get there from Nice, along a very scenic route through the Vallée de la Tinée river.
Auron is about 2 hours from Nice, about 30mins further up the road from Isola. Whereas Isola 2000 begins at an altitidue of 2000m, the ski pistes of Auron start at an altitude of 1600 m. At this lower altitude, it is obviously more susceptible to higher temperatures. Auron, near the village of Saint-Étienne-de-Tinée, is also located in a very scenic area, and most definitely worth a visit in summer too - mountain biking, hiking, etc.
Of all the regional ski fields, Greolières-les-Neiges lies at the lowest altitude, at 1400m above sea level. No surprise therefore that this resort has a much shorter opening season that those at a higher altitude. Greolières is excellent for people with families and for the absolute beginners. It lies in the pre-Alps behind Grasse, about 1h30 from Nice, and some 45mins from Grasse.
Here too, the scenic area allows for plenty of exploration and outdoor activities in summer. Link: Greolières-les-Neiges.
Another very popular resort, at 1700m altitude, and about 1h30 from Nice. Probably the most family friendly, and lots of out-of-season activities. Link: Valberg.com.