Mi padre quiere dejarse barba en invierno.

Because dejarse is the natural Spanish way to say to let oneself grow something like a beard, hair, or moustache.

So:

• dejar = to leave, to let
• dejarse barba = to let oneself grow a beard

The se refers back to the subject, here mi padre. In English we usually do not say let himself grow a beard, but Spanish often does.

Compare:

• Mi padre quiere dejarse barba. = My father wants to grow a beard.
• Mi padre quiere dejar la barba. = This would mean something different, more like leave the beard.

So the se is important.

In Spanish, when you have a conjugated verb plus an infinitive, object pronouns and reflexive pronouns can often go in two places:

• before the conjugated verb
• attached to the infinitive

So both of these are correct:

• Mi padre quiere dejarse barba.
• Mi padre se quiere dejar barba.

They mean the same thing.

Spanish often sounds very natural with the pronoun attached to the infinitive, especially in sentences like this.

Spanish can use barba without an article in this expression when it means a beard / beard in general.

So:

• dejarse barba = to grow a beard, to wear a beard

This is a fairly idiomatic expression.

If you say dejarse la barba, that is also possible, and many speakers use it. It can sound a bit more like grow out his beard or let his beard grow, referring to the beard as something belonging to him.

Very roughly:

• dejarse barba = grow a beard / wear a beard
• dejarse la barba = let his beard grow / grow out the beard

In everyday use, both can be heard.

Yes. This is a very common pattern:

• querer + infinitive = to want to do something

Examples:

• Quiero comer. = I want to eat.
• Quiere salir. = He/She wants to go out.
• Mi padre quiere dejarse barba. = My father wants to grow a beard.

Only querer is conjugated here:

• quiero
• quieres
• quiere
• queremos
• queréis
• quieren

The second verb stays in the infinitive: dejarse.

In Spanish, family words are often used with a possessive like mi, tu, su when you mean my father, your mother, etc.

So:

• mi padre = my father
• mi madre = my mother

Spanish can also use the definite article in some contexts, especially when talking about family members generally or in certain styles:

• El padre de Juan... = Juan’s father...
• Mi padre... = My father...

For a basic sentence like this, mi padre is the normal and natural choice.

En invierno means in winter or during winter.

It can refer to:

• winter in general
• what someone usually does in that season
• what someone plans to do when winter comes

In this sentence, it most naturally means something like during the winter months.

Other seasons work the same way:

• en verano = in summer
• en otoño = in autumn
• en primavera = in spring

Yes, depending on context, en invierno can sometimes suggest a habitual idea like in winter / during wintertime, which could be understood as something he tends to do each winter.

But by itself, the sentence does not force that meaning. It could also mean just one coming winter.

If you wanted to make every winter clearer, you could say:

• todos los inviernos = every winter
• cada invierno = each winter

For example:

• Mi padre se deja barba cada invierno. = My father grows a beard every winter.

It usually means to let a beard grow, so the focus is on the action or decision not to shave.

In practice, though, it can also imply the resulting state: to wear a beard.

So if someone says:

• Se dejó barba.

that often means:

• He grew a beard
• or He started wearing a beard

The idea is not that the beard appeared instantly, but that he allowed it to grow.

It is understandable and quite natural, but there are a few very common alternatives in Spain:

• Mi padre quiere dejarse barba en invierno.
• Mi padre quiere dejarse la barba en invierno.
• Mi padre quiere dejarse crecer la barba en invierno.

These are all possible.

Very roughly:

• dejarse barba = a compact, idiomatic way to say grow a beard
• dejarse la barba = also very common
• dejarse crecer la barba = a bit more explicit, literally let his beard grow

A learner is most likely to hear either dejarse barba or dejarse la barba.

Yes. This structure is very common with hair and facial hair.

Examples:

• dejarse bigote = to grow a moustache
• dejarse perilla = to grow a goatee
• dejarse el pelo largo = to grow one’s hair long
• dejarse el pelo = to let one’s hair grow

So the pattern is useful beyond barba.

Because Spanish normally leaves out subject pronouns when the verb ending already makes the subject clear.

Here we already have mi padre, so adding él would be unnecessary:

• Mi padre quiere dejarse barba... = natural
• Él, mi padre, quiere dejarse barba... = possible only for emphasis or contrast, but not normal here

Spanish often avoids repeating the subject when it is already obvious.

Yes, Spanish word order is flexible, so you could move en invierno for emphasis.

For example:

• Mi padre quiere dejarse barba en invierno. = neutral
• En invierno, mi padre quiere dejarse barba. = puts more focus on in winter

Both are correct. The original order is the most neutral and straightforward.