It's а tough question. ¶
I don't like sunny weather because it's usually boiling hot.

I love cloudy and windy weather. / I love it when it's cloudy and windy.

Indeed, I can't stand snowingy weather, because iI must cleaned my house's outdoors the outside of my house, but iI like rain.

I don't think we say "house's outdoors."

I think, rainy weather has a mysteryious vibe.

And iI like thunderstorms.

I adore to photograph aing lightning, but thunder often sounds very loud.

By the way, my dog doesn't like thunderstorms.. mMy dog is afraid itof them.

What wWeather dDo yYou lLike?

Important words in title have capital letters. Question so needs question mark.

It's а tough question. ¶
I don't like sunny weather because it's usually boiling hot.

Need a full stop between the two sentences.

iIt isn't hot.

Sentences start with a capital letter.

Indeed, I can't stand snowingy weather, because iI must cleaned my house's outdoors the outside of my house, but iI like rain.

Do not think you need the "indeed". "snowy weather" is the phrase. "I must clean" with must you use the infinitive minus the "to" part. First person singular pronoun is "I" i.e. capitalised. It is "the outside of my house". "Outdoors" is not part of your house. So "the dog is outdoors".

I think, rainy weather has a mysteryious vibe.

Don't need the comma. The adjective is "mysterious". Run into next sentence.

Aand iI like thunderstorms.

To describe generally liking something use the plural. "I like thunderstorms", "I like dogs", "I like children".

I adore to photograph aing lightning, but thunder often sounds very loud.

Use the present participle after "adore" not the infinitive form. Lightning is uncountable in English so no indefinite article. A single instance is "a bolt of lightning" or "a flash of lightning".

BMy the way, my dogdog, however, doesn't like thunderstorms.. my dog He is afraid itof them.

Think it sounds more natural this way. Phrase "to be afraid of X". "thunderstorms" is plural so pronoun is "them" in this instance.