Learn English – Can ‘enquire’ or ‘inquire’ be used without a preposition

You can safely omit it pretty much always.

I think it's largely a regional variety issue. As the article explains, in the UK "I've got" might be used more commonly where Americans would say "I have".

I remember being taught phrases like this in elementary English classes (due to British English emphasis in Finnish schools at that time):

I've got a cat.

But rest assured, it is never wrong to omit "got" in a phrase like this and just say:

I have a cat.

Also in those cases where it's used to add emphasis or indicate obligation...

I've got to go now!

... you can always omit it and still be perfectly understood (you can add the emphasis in other ways):

I have to go now!

Your sentence doesn't say what you want it to say, so before answering the question, I'll have to rewrite it in idiomatic English:

I don't like autumn, to be honest, nor do I like the winter that comes after it.

One problem is that prepositional phrase "to be honest", which describes your feeling in my rewrite (I've added a comma to make the phrase parenthetical and to prevent the reader from believing that it's supposed to modify "autumn") but modifies "autumn" in your sentence and means "I don't like it when autumn is honest", a meaningless (unless metaphorical and poetic) statement. The other problem is that "neither" should probably be "nor", but both are possible with different punctuation.

To invert the subject and verb without adding "do" is not natural English:

*I don't like autumn, to be honest, nor like I (the) winter that comes after it.
*I don't like autumn, to be honest; neither like I (the) winter that comes after it.

Idiomatic English would be:

I don't like autumn, to be honest, nor do I like the winter that comes after it.
I don't like autumn, to be honest; neither do I like the winter that comes after it.

or

To be honest, I don't like autumn, nor do I like the winter that comes after it.
To be honest, I don't like autumn; neither do I like the winter that comes after it.

It isn't just a matter of grammar. Style demands parallel structure here. Perhaps in German it's possible to invert the subject and verb, but English grammar has changed significantly since it might have been possible to do that more than 1000 years ago.

Google translate gave me this for English => German:

*I don't like autumn, nor like I winter
Ich mag es nicht im Herbst, noch mag ich im Winter (But I'm not certain that this is real German, so I make no claims about it other than the subject and verb have been inverted).