Snowshoeing is only available in the winter months, as there is no snow during spring and summer. Most tour companies operate according to that day's forecast, and there is a chance the outing could be called off if there is a risk of avalanche.
It is worth booking your Cortina d'Ampezzo accommodation well ahead, as the town is a popular choice during ski season.
Before you book your tour make sure the fitness requirements match your level – you don't want to find yourself stuck 3 hours into the hike!