>>1648207it's very possible and you have plenty to choose from and do, but it's really up to your own interpretation of cheap and the difficulty you choose to play the game on
[i'm too young to die] all-inclusive type packages from travel agencies (cheapest are either last minute deals or booked 6-12 month prior), with or without transport, you're all set in terms of sleeping, eating and ski passes, equipment, cable rides, and what-not, hotels are usually either right next to the slope or offer regular transport to it, everybody speaks english, you'll meet plenty of foreigners to do shit together with, you can book multiple back to back so you'll just have to go from one place to the next, you'll also probably have some sort of 'tourist night' experience with traditional food and dancing, it's the most expensive but still way cheaper than its western counterpart
best for beginners until you get the hang of things
[hurt me plenty] direct reservation at the hotel,
booking.com or airbnb (the latter is really popular in fortified mountain cities like brasov, sibiu or cluj), you may pay some extra to the intermediary site if used, quite likely there won't be any problem with the language barrier at the hotels but asking for directions might not always be so easy, you get to decide on the spot and individually what you want to do and where you want to go (eat, walk, visit)
if you already have experience traveling, you'll do just fine in youth hostels, generally the youth all speak english and are very willing and proud to help