A Natale ceniamo tutti insieme a casa della nonna.

A Natale is a common Italian time expression meaning at Christmas / on Christmas.

Italian often uses a with major holidays:

• a Natale = at Christmas
• a Pasqua = at Easter

Putting A Natale at the beginning sets the time frame first, like saying At Christmas, ... in English.

In the fixed expression a Natale, Italian normally does not use an article.

Compare:

• A Natale ceniamo insieme. = At Christmas we have dinner together.
• Il Natale è importante per molte famiglie. = Christmas is important for many families.

So:

• Natale with no article is normal in this kind of time phrase.
• il Natale is used when talking about Christmas as a holiday in general.

Italian often uses the present tense for:

• habitual actions
• traditions
• scheduled or expected future events

So ceniamo can mean:

• we have dinner (habit/tradition)
• we’re having dinner (planned future)

In this sentence, it sounds very natural because Christmas dinner is a repeated family tradition or a planned event.

Italian usually drops subject pronouns when they are clear from the verb ending.

Ceniamo already means we have dinner, because -iamo marks we.

So:

• Ceniamo = we have dinner
• Noi ceniamo = we have dinner, with extra emphasis

You would add noi only if you want contrast or emphasis, for example:

• Noi ceniamo a casa della nonna, loro al ristorante.
  = We have dinner at grandma’s house, they at the restaurant.

Ceniamo comes from cenare, which means to have dinner.

It is more specific than mangiare:

• mangiare = to eat
• cenare = to dine / to have dinner

So the sentence is specifically about the evening meal, not eating in general.

Both words add something:

• tutti = all of us / everyone
• insieme = together

So tutti insieme means all together.

You could say:

• ceniamo insieme = we have dinner together
• ceniamo tutti = we all have dinner

But ceniamo tutti insieme is stronger and more natural for the idea of the whole group being together in one place.

Tutti is the masculine plural form, which Italian uses for:

• mixed groups of males and females
• groups where the gender is not specified

If the group were entirely female, you would say:

• ceniamo tutte insieme

So tutti insieme is the normal default if the family group includes men and women or if the speaker is not specifying.

Because a casa di... is a fixed Italian expression meaning at someone’s house / at someone’s place.

So you say:

• a casa mia = at my house / at my place
• a casa di Luca = at Luca’s house
• a casa della nonna = at grandma’s house

Using alla casa would sound like you are talking about the physical house as a building in a more literal way, not the normal idea of being at someone’s home.

Della is a contraction of:

• di + la = della

Here it means of the.

So literally:

• a casa della nonna = at the house of the grandmother

But in natural English, that becomes:

• at grandma’s house
• at grandma’s

This is a very common structure in Italian.

Literally, it means of the grandmother, but in real usage it often simply means grandma’s, with the exact relationship understood from context.

Italian often uses family words this way:

• la mamma
• il papà
• la nonna

Depending on context, these can naturally refer to mom, dad, grandma, not just some random mother/father/grandmother.

If you wanted to be more explicit, you could say:

• a casa di mia nonna = at my grandmother’s house

But a casa della nonna is completely natural when the family relationship is already clear.

Yes. Italian word order is fairly flexible.

This sentence begins with A Natale because the speaker wants to highlight the time first:

• A Natale ceniamo tutti insieme a casa della nonna.

You could also say:

• Ceniamo tutti insieme a casa della nonna a Natale.

That is grammatically possible, but it sounds a little less natural in many contexts because the time expression comes as an afterthought. Starting with A Natale is smoother and very common.