K horské chatě se dá jít zkratkou.

Because k means to / toward / up to, and it takes the dative case.

So:

• k chatě = to the hut, toward the hut, up to the hut
• do chaty = into the hut

In this sentence, the idea is reaching the mountain hut as a destination, not going inside it. That is why k is used.

Because k requires the dative case, and chata is a feminine noun.

The basic form is:

• chata = hut

After k, it changes to the dative singular:

• k chatě = to the hut

So the sentence uses:

• k horské chatě = to the mountain hut

The adjective has to match the noun in gender, number, and case.

Here:

• chata is feminine singular
• after k, it is in the dative singular
• so the adjective must also be feminine singular dative

That gives:

• horská chata = mountain hut
• k horské chatě = to the mountain hut

So horská changes to horské because of the case.

Se dá jít is an impersonal Czech expression meaning something like:

• one can go
• it is possible to go
• you can go

It comes from dát se + infinitive.

Very literally, dá se means something like it gives itself / it can be done, but in normal English we translate it more naturally as can or it is possible to.

So:

• K horské chatě se dá jít zkratkou. = You can get to the mountain hut by taking a shortcut.

Czech often uses impersonal constructions where English would use you, one, or a passive-style expression.

In this sentence, no specific person is meant. It means something general:

• people can go
• you can go
• it is possible to go

So the sentence is not about one particular person. It is a general statement about what is possible.

Jít means to go on foot / to walk.

So this sentence suggests reaching the hut by walking.

That fits well with zkratkou (by a shortcut), because shortcuts are often walking routes.

If the sentence were about going by vehicle, Czech would probably use a different verb, such as jet.

Zkratkou is the instrumental singular of zkratka.

• zkratka = shortcut
• zkratkou = by means of a shortcut / via a shortcut

The instrumental is often used in Czech to express:

• means
• manner
• route

So jít zkratkou means:

• to go by a shortcut
• to take a shortcut

Because Czech often uses the instrumental case by itself to express the way something is done.

So:

• jít zkratkou = go by a shortcut
• jet vlakem = go by train
• psát tužkou = write with a pencil

English often needs a preposition like by or with, but Czech can express that meaning just through the instrumental ending.

Yes. That would also be correct.

Czech word order is fairly flexible. The sentence can be rearranged depending on what you want to emphasize.

For example:

• K horské chatě se dá jít zkratkou.
• Dá se jít k horské chatě zkratkou.

Both mean essentially the same thing.

The version with K horské chatě first puts the destination in focus first.

Se is a short unstressed word, and Czech usually places these short words in a special position near the beginning of the clause.

That is why you get:

• K horské chatě se dá jít zkratkou.

not usually something like:

• K horské chatě dá se jít zkratkou.

So this placement is mainly about normal Czech clitic word order.

Sometimes yes, but the nuance is a little different.

• dá se jít = it is possible / feasible / doable to go
• může se jít = one may go / it is possible to go

In many contexts they are close, but dá se often sounds very natural when talking about practical possibility.

Here, se dá jít zkratkou suggests that there is a workable way to get there by a shortcut.

Yes. Horská chata is a common Czech expression for a mountain hut, mountain lodge, or cabin in the mountains.

Depending on context, English could translate it as:

• mountain hut
• mountain cabin
• mountain lodge

But grammatically in the sentence, it behaves simply as:

• horská chata → k horské chatě

Here are the dictionary forms:

• k = to, toward
• horský = mountain, mountainous
• chata = hut, cabin
• se = reflexive particle
• dát se = to be possible, to be doable
• jít = to go on foot
• zkratka = shortcut

So the sentence is built from very common Czech words and one very common impersonal pattern: dá se + infinitive.