Rachel and Bob have already done a good job with corrections. I just add the following: 

- We don't normally say "We had snowfall". It sounds awkward/cute :) Normally we would say "We have snow!" or "It snowed last night!" If you really want to use "snowfall" then the phrasing that feels most natural to me is "We have had a snowfall!" But I don't think I've ever heard anyone use these words in this way; while it's technically correct it's not the way the language is usually used. 

Snow, so much snow

We had a snowfall! I woke this morning and saw that everything was white outside the window. Snow has stuck everywhere, it was on the branches of trees, on cars, on a fence...
In the town, there was a big traffic jam, cars could not  move normally because of snowdrifts, but on the other hand the street was very beautiful.
In the photo is the view from my window.

Hello Sasha,

You certainly did get some snow, didn't you. As you are writing this in the evening the morning is finished so you should use the past simple - finished action in finished time - and not the present perfect which is action in unfinished time. Apart from that just be careful with the article 'a' -  it means one so you can't use it with plural nouns - cars, branches ...

Hope this helps

Bob

Snow, so much snow

We had snowfall! I have awoken awoke/woke up in the this morning today and have seen saw that all everything was white outside the window. Snow has was stuck everywhere,! it was on a tree branches of trees, on a cars, and on a fences...
In the town has happened there was a big traffic jam, cars could not normal move normally because of drifts, but on the other hand, the street was very beautiful
On The photo is shows the view from my window

:)