The house I stayed hasd a sauna , so I went to the sauna for the first time. The house I stayed had a sauna, so I went to the sauna for the first time.

Everything has to be in past tense, even though, yes, the house still technically has the sauna.

I thought I wouldn't sweated because my body [ just got hot, right off I was in sauna room , ] but Ithat wasn't what happened. I thought I wouldn't sweat because my body [ just got hot, right off I was in sauna room, ] but that wasn't what happened.

I'm not 100% sure what you mean in the part I put between the square brackets []

I sweated a lot . I sweated a lot.

I want to go a sauna in Japan and try to compare the difference. I want to go a sauna in Japan and try to compare the difference.

I went to the market and it hasd many Moomin products and other famous stuff. I went to the market and it had many Moomin products and other famous stuff.

Everything has to be in past sentence.

I bought two moomin mugs and some tea. I bought two moomin mugs and some tea.

Mugs --> you need the S as its plural You could just say "tea", but I think "some tea" sounds better here

I also went to the Santa Clause village . I also went to the Santa Clause village.

We don't put a space before the period/full stop in English.

My family (including me) was suprised how depth ofep the snow was. My family (including me) was suprised how deep the snow was.

Or: "...was surprised by the depth of the snow."

SThe snow was soft and when I moved my feet to walk forward, The snow was soft and when I moved my feet to walk forward,

"Moved" to match the past tense.

Ithey sank in snow and I couldn't go forward as fast as I move usually can. they sank in snow and I couldn't go forward as fast as I usually can.

They = because you have 2 feet, it as to be plural No need for a capital letter as this is still part of the previous sentence, seperated only by a comma (,)

I struggled to move my feet because it was hard to　 get out of the snow. I struggled to move my feet because it was hard to get out of the snow.

I playedwent sledding and it became one of my favorite snow playactivities. I went sledding and it became one of my favorite snow activities.

We usually "go sledding", "go skiing", "go snowboarding", etc rather than "play" any of them I changed it to activity for the same reason

My siblings were also love thisd it. My siblings also loved it.

No need for the "were" here