The balcony door is not properly sealed.
te-NU-ta — three syllables, stress on the second. 'Tenuta stagna' = airtight seal.
When cold air, rain, or street noise enters through the gaps around a balcony door or French window.
'A tenuta stagna' (airtight) is a technical expression meaning 'hermetically sealed'. 'Non è a tenuta stagna' = is not airtight. A more everyday alternative is 'entra aria dalla porta' (air comes in through the door). Use whichever feels comfortable.
Entra freddo dalla porta del balcone.
Cold air comes in from the balcony door.
Simpler and equally effective description of the problem
Sento spifferi dalla finestra.
I can feel draughts from the window.
'Spiffero' = draught — a very common Italian word for this specific problem
Quando piove entra l'acqua dal balcone.
When it rains, water comes in from the balcony.
A more serious structural problem requiring immediate attention
Old Italian double-glazed windows and French doors ('porte finestre') in historic buildings often have worn rubber seals that let in cold air and noise. This is a very common problem in Italy, where many hotels are in converted medieval or Renaissance buildings with retrofitted windows.