Not necessarily! The most important thing is not over-pushing yourself. The last thing you want to do is tire yourself out and not have the stamina for the rest of your trip. So take it as it comes and focus on enjoying yourself most of all!
And if you choose one of the many amazing resorts that cater to non-skiing activities, you'll have countless other things that you can do, from heading to high altitude viewing points to ice skating and even swimming in the many high altitude swimming pools (who says you shouldn't treat yourself to a hot-tub while on holiday!)