Хоть на улице и холодно, мне всё равно хочется немного погулять в парке.

Хоть ... и is a common Russian pattern meaning although / even though.

So:

• Хоть на улице и холодно = Although it’s cold outside

The и here does not mean a separate and. It is part of the concessive pattern and helps emphasize the contrast.

A very similar alternative is:

• Хотя на улице и холодно...

In this sentence, хоть sounds a bit more conversational.

Yes, literally на улице is on the street, but in everyday Russian it very often means outside / outdoors.

So:

• На улице холодно = It’s cold outside

It does not necessarily mean you are physically standing in a street. It is just the normal idiomatic way to talk about outdoor weather.

Because холодно here is not an adjective describing a noun. It is a predicative word expressing a state or condition:

• На улице холодно = It is cold outside

There is no noun being described, so Russian uses холодно.

Compare:

• На улице холодно. = It’s cold outside.
• Улица холодная. = The street is cold.

The second sentence describes улица as a noun, so it uses the adjective холодная. The original sentence does not do that.

In the present tense, Russian usually omits the verb to be.

So:

• На улице холодно literally looks like Outside cold
• but it means It is cold outside

This is completely normal Russian.

If you put it in the past or future, the verb appears:

• На улице было холодно. = It was cold outside.
• На улице будет холодно. = It will be cold outside.

This is a very common question.

• Я хочу = I want
• Мне хочется = I feel like / I have a desire to

So мне хочется is usually a bit softer, less direct, and more about a spontaneous feeling.

In this sentence:

• мне всё равно хочется немного погулять
  = I still feel like taking a little walk

Grammatically, хочется is used impersonally, and the person experiencing the feeling appears in the dative:

• мне = to me

That is why it is мне хочется, not я хочется.

Here всё равно means all the same / anyway / still.

So the idea is:

• It’s cold outside, but I still feel like going for a walk.

Important: in other contexts, мне всё равно can mean I don’t care. But in this sentence, that is not the meaning.

Here it modifies хочется:

• мне всё равно хочется = I still feel like / I want to anyway

So it expresses persistence despite the cold.

Немного means a little / a bit.

Here it softens the action:

• немного погулять = to walk a little / to go for a short walk

It suggests a small amount of time or a light, casual action, not a long serious walk.

Гулять is the basic verb meaning to walk / stroll / spend time out walking.

Погулять is the perfective form with the prefix по-, and here it often gives the meaning to walk for a while / to take a short walk.

So:

• гулять = walking in general, or the process of walking
• погулять = go for a walk for some time, as a complete little activity

That works very naturally with немного:

• немного погулять = to take a short walk

В парке means in the park and gives the location of the walk.

So:

• погулять в парке = to take a walk in the park

You could also say:

• погулять по парку

That means more like to walk around the park or walk through the park, with a stronger sense of movement around inside it.

So the difference is:

• в парке = location
• по парку = movement around the area

Both are possible, but the original sentence simply focuses on where the walk would happen.

Because this sentence has two clauses:

1. Хоть на улице и холодно
2. мне всё равно хочется немного погулять в парке

The first clause is a concessive clause: although it’s cold outside. Russian separates it from the main clause with a comma.

So the structure is:

• Although X, Y

That is why the comma is needed.

Yes, absolutely.

That version is also correct:

• Хотя на улице холодно, мне всё равно хочется немного погулять в парке.

This is very close in meaning to the original sentence.

A rough comparison:

• хоть = a bit more conversational
• хотя = neutral and very common

You may also see:

• Хотя на улице и холодно, мне всё равно хочется немного погулять в парке.

So both хоть and хотя work here.