Can one carry on Shabbos on the grounds of a hotel that is privately enclosed for only people that are staying in the hotel?
Answer:
It is permitted to carry in a hotel that has a common dining room where everybody eats together, or where all the food comes from a communal kitchen, even if some eat in different rooms.
If (Jewish) people eat their own food for meals, it will be required to make an Eiriv Chatzeros. This is relatively easy if all residents are observant Jews (ownership of a box of matzos is transferred to all residents), but if there are also non-Jews or non-observant Jews it can be a little more complex (a token payment must be given to the hotel owner as "rental" of the hotel before the Eiruv is made).
However, if the owner of the hotel reserves the right to move visitors from room to room, one can be lenient and not require an Eiruv (Minchas Yitzchak 4:55; Maharsham 5:36).
Best wishes.
Sources:
For details of this issue please see here (Hebrew)