На мокрой траве было холодно сидеть, поэтому мы перешли с поляны на сухой песок у воды.

Because Russian often uses an impersonal construction to talk about conditions or how something feels.

• было холодно сидеть = it was cold to sit / it was too cold to sit
• There is no grammatical subject in this clause.
• было is the past tense of быть, used here in a neutral, impersonal way.
• холодно is not an adjective here; it is a predicative adverb/state word, meaning cold as a condition.
• сидеть is the infinitive to sit and explains what was cold.

So the structure is basically:

• [place] + было + холодно + infinitive

This is a very common Russian pattern:

• Здесь было трудно работать. = It was hard to work here.
• Мне было скучно ждать. = It was boring for me to wait.

Here на means on, in the sense of location, so it takes the prepositional case.

• трава = grass
• на траве = on the grass

Because трава is feminine singular, the prepositional singular form is:

• трава → траве

And the adjective must agree with it:

• мокрая трава → на мокрой траве

So:

• на мокрой траве = on the wet grass

Because it agrees with траве, which is:

• feminine
• singular
• prepositional case

The adjective мокрый changes to match the noun:

• masculine nominative: мокрый
• feminine nominative: мокрая
• feminine prepositional: мокрой

So:

• мокрая трава = wet grass
• на мокрой траве = on the wet grass

This agreement of adjective + noun is one of the core patterns in Russian grammar.

Because Russian often does not use a dummy subject like English it.

English says:

• It was cold to sit on the wet grass.

Russian simply says:

• На мокрой траве было холодно сидеть.

The sentence is understood as impersonal: the situation itself was cold/uncomfortable. Russian does this very naturally with weather, conditions, and general states:

• Было темно. = It was dark.
• Было жарко. = It was hot.
• Было трудно понять. = It was hard to understand.

So the missing it is completely normal.

Because the sentence describes movement from one place to another:

• с поляны = from the clearing
• на сухой песок = onto the dry sand

Different prepositions show different parts of the movement:

1. с + genitive = movement off/from

   • с поляны = from the clearing

2. на + accusative = movement onto/to

   • на сухой песок = onto the dry sand

So the whole idea is:

• we moved from the clearing onto the dry sand

This is a very common contrast in Russian:

• на столе = on the table (location)

• на стол = onto the table (direction)

• с стола = from the table

Because с in the sense of from/off takes the genitive case.

The noun is:

• поляна = clearing, glade

Its genitive singular form is:

• поляны

So:

• с поляны = from the clearing

This is the same pattern as:

• с улицы = from the street
• с горы = from the mountain
• с работы = from work

Because this sentence expresses motion toward a destination, not location.

Compare:

• на сухом песке = on the dry sand, located there
• на сухой песок = onto the dry sand, moving there

Russian uses:

• на + prepositional for location
• на + accusative for motion toward something

Here the verb перешли means moved/went over, so a destination is needed:

• мы перешли на сухой песок = we moved onto the dry sand

Because песок is:

• masculine
• singular
• inanimate

For most inanimate masculine nouns, the accusative singular is the same as the nominative singular.

So:

• nominative: сухой песок
• accusative: на сухой песок

That is why nothing seems to change here.

Compare with an animate masculine noun, where accusative usually matches genitive:

• я вижу брата = I see my brother

But with inanimate nouns:

• я вижу стол = I see a table

у воды means by the water, near the water, or at the water’s edge.

The preposition у usually means by, near, beside and takes the genitive case.

• вода = water
• genitive singular: воды

So:

• у воды = by the water

This phrase does not mean in the water. For that, Russian would use в воде.

Compare:

• у воды = by the water
• в воде = in the water

поэтому means therefore, so, or that’s why.

It connects the two parts logically:

• It was cold to sit on the wet grass,
• so/therefore we moved to the dry sand.

It is very common in spoken and written Russian.

Examples:

• Я устал, поэтому пошёл домой. = I was tired, so I went home.
• Шёл дождь, поэтому мы остались дома. = It was raining, so we stayed home.

In this sentence, поэтому introduces the result of the situation in the first clause.

перешли is the past plural form of перейти, a perfective verb meaning something like:

• to cross
• to move over
• to go from one place to another

Here it suggests changing position from one surface/area to another:

• from the clearing
• to the dry sand by the water

It sounds more specific than simply пошли (went).
перешли often implies a transition from one side/zone/place to another.

For example:

• Мы перешли дорогу. = We crossed the road.
• Мы перешли в другую комнату. = We moved into the other room.

So in this sentence it gives the sense of shifting over to a better spot.

Because было belongs only to the first, impersonal clause:

• На мокрой траве было холодно сидеть

That clause has no subject, so Russian uses the neuter singular past form было.

Then the second clause has its own subject and verb:

• поэтому мы перешли...

So the sentence is really two separate parts:

1. На мокрой траве было холодно сидеть
   = It was cold to sit on the wet grass.

2. поэтому мы перешли...
   = so we moved...

The мы does not control было.

Yes. Russian word order is fairly flexible, although the original order sounds natural and clear.

Original:

• На мокрой траве было холодно сидеть, поэтому мы перешли с поляны на сухой песок у воды.

This starts with the setting: on the wet grass. That is a very natural way to present the situation.

Other possible orders include:

• Было холодно сидеть на мокрой траве, поэтому мы перешли с поляны на сухой песок у воды.

This version is also correct. It puts the focus first on it was cold to sit.

So the original word order is not the only possible one, but it is a very normal and idiomatic choice.

Because сидеть makes the meaning more specific.

• На мокрой траве было холодно could mean something like it was cold on the wet grass there
• На мокрой траве было холодно сидеть clearly means it was cold to sit on the wet grass

So the infinitive explains exactly what action was uncomfortable.

Russian often uses this structure:

• было трудно идти = it was hard to walk
• было приятно смотреть = it was pleasant to watch
• было опасно оставаться = it was dangerous to stay

Here:

• было холодно сидеть = it was cold to sit

Not strictly necessary for basic meaning, but it adds a helpful detail.

Without it, you could say:

• ...поэтому мы перешли на сухой песок у воды.
• ...so we moved onto the dry sand by the water.

That already works.

But с поляны adds the specific starting point:

• they moved from the clearing

So it gives a fuller picture of the scene. Russian often includes this kind of from X to Y detail when describing motion:

• с поляны на песок
• с дороги в лес
• с берега в воду

It makes the movement more vivid and precise.