En verano prefiero las chanclas, pero para caminar mucho llevo zapatillas cómodas.

Because Spanish normally uses en with seasons to mean in / during that season.

• en verano = in summer
• en invierno = in winter

For a general statement like this, en verano is the most natural choice. You may also hear en el verano in some contexts, but en verano is the standard, simple way to say it.

Prefiero is the yo form of preferir in the present tense:

• yo prefiero
• tú prefieres
• él/ella prefiere
• nosotros preferimos
• vosotros preferís
• ellos/ellas prefieren

This verb is a stem-changing verb: e → ie in most forms, but not in nosotros or vosotros.

So here, prefiero means I prefer.

This is a very common thing learners notice.

In prefiero las chanclas, the definite article is used to talk about a whole category in a general way. Spanish often does this where English would use no article:

• Prefiero las chanclas = I prefer flip-flops

But with llevo zapatillas cómodas, Spanish often drops the article when talking about what someone is wearing:

• llevo zapatillas cómodas = I wear comfortable sneakers / I’m wearing comfortable sneakers

So the difference is not random:

• preferir + article is very common for general preferences
• llevar + clothing item often appears without an article when the item is indefinite or generic

You could also say llevo unas zapatillas cómodas if you want to emphasize a pair of comfortable sneakers.

In Spain, chanclas usually means flip-flops or very casual open footwear, especially for the beach, pool, or hot weather.

They are more informal than sandalias:

• chanclas = flip-flops / slides / very casual beach footwear
• sandalias = sandals in general

So chanclas gives a very summery, casual feeling.

Yes, llevar often means to carry, to take, or to bring, but with clothes, shoes, and accessories it very often means to wear.

So:

• llevo zapatillas cómodas = I wear comfortable sneakers / I’m wearing comfortable sneakers

This is extremely natural in Spanish.

Compare:

• llevo una chaqueta = I’m wearing a jacket
• lleva gafas = he/she wears glasses

A learner might think of usar, but in Spain llevar is usually more idiomatic here.
Me pongo would mean I put on, which focuses on the action of putting them on, not on wearing them as your choice.

In Spain, zapatillas usually means sneakers, trainers, or casual sporty shoes.

In this sentence, because of para caminar mucho, it clearly means comfortable walking shoes or sneakers, not slippers.

This word can vary by region in the Spanish-speaking world, so it is worth remembering that this is a good Spain Spanish usage.

Cómodas agrees with zapatillas.

• zapatillas is feminine plural
• so the adjective must also be feminine plural: cómodas

Agreement:

• zapato cómodo = comfortable shoe
• zapatos cómodos = comfortable shoes
• zapatilla cómoda = comfortable sneaker
• zapatillas cómodas = comfortable sneakers

As for position, Spanish usually puts descriptive adjectives after the noun:

• zapatillas cómodas
• casa grande
• libro interesante

Putting the adjective before the noun is sometimes possible, but it often sounds more literary, emotional, or marked. Here, zapatillas cómodas is the normal order.

It gives the purpose or use of the shoes.

• para = for / in order to
• caminar mucho = to walk a lot

So para caminar mucho means:

• for walking a lot
• if I’m going to walk a lot

This structure is very common:

• zapatos para correr = shoes for running
• agua para beber = water for drinking
• una mochila para viajar = a backpack for traveling

Because mucho here means a lot, not very.

• caminar mucho = to walk a lot
• muy is used before adjectives or adverbs, not directly like this with the meaning a lot

Compare:

• camino mucho = I walk a lot
• es muy cómodo = it is very comfortable

So in this sentence, mucho is the correct word.

Yes, in many situations you could say andar.

• para caminar mucho
• para andar mucho

Both can work. In many varieties of Spanish, andar is very common in everyday speech.
But caminar is clear, standard, and easy for learners to understand, so it fits very well here.

Not usually in Spain.

In Spain, the most natural options are:

• zapatillas
• zapatillas deportivas
• deportivas

In some Latin American countries, tenis is used for sneakers, but that is not the normal Spain Spanish choice.

So for Spain, this sentence sounds natural as it is:

• llevo zapatillas cómodas