For our trip, we decided to mtake the journey day by day.

"Take it day by day" is the common phrase that I believe you're looking for here.

When I looked at the map, I found a place that name isd Seiryu-ji temple, not far from Aomori, so we went there.

During the trajetOn the way there, we were astonished by the heavy layer of snow, but all ththe entire road was perfectcompletely cleanr.

"On the way" is more natural. "There" is where you are going. To emphasize how much snow, I would include "heavy" to mean a lot of snow. "Clean" here could sound like the opposite of dirty, where "clear" meaning without obstacles would sound better.

When we arrived, I thought that it was closed, because we were the only car oin the parking lot.

Make sure to include a subject to answer the question "what was closed?". Since you entered the place, you are "in" the place where you park. We call this a "parking lot".

SoBut we went benearto the gates and we saw it was open.

To contrast your previous sentence, you can use "but" or "however".

First off, I foundsaw the big gates, the Sanmon, which was very impressive by the height and the details of. The gate was very tall and the statues of gods were very detailed.

I would split this into two sentences, and clarify what specific parts I am describing.

We followed the way until thepath up to reception, and we were surprised because the receptionist asked us to paidy for the visit.

We don't know who "he" is, so I assume you are talking about the person at reception: "the receptionist". Since you are talking about the event as it happened, he asked you to "pay" in that moment.

It was a surprise because, in France, the visit ofing churches areis free, so we thought it was the same thing in Japan.

AIt was a really peaceful place.

You could combine this with the previous sentence or make it stand alone like the correction.

In spring and summer, it's possible to see monkeys, but with the snow, they were not there.

To be clear you are talking about the temple you visited, you would say "there". If you said here, it sounds like you are talking about the place you're currently in.

The fountain didn't work because the water could be freeozen in this season.

There was a lot of little statues which refer tosymbolized foetuses who unfortunately lost lifedied and we could pray for them.

Symbolized means it acts as a symbol. You could say "died" or for a nicer sounding phrase, "passed away".

But the most impressive things was the massive statue of a Buddha, thaand it was possible to visited him inside.

Moreover, the inside was dedicated to the zodiac chineseChinese zodiac and each sign was linked to a Buddha.

"chinese" should be capitalized here since it's the name of place: a proper noun.

We didn't know we cwould be find something like that on this placthere.