You still have daily freezes...YIKES. Apples are very hardy even to spring freezes. So that could be the issue but probably not. Was there freeze damage on anything else? Is it still firmly anchored in the ground?

It looks like it froze, got broken off, or gophers severed the stem/roots below ground.

There was freeze damage to some of the bulbs in same area of yard. Other apple, which is hardy for zone 4 is happy, no damage. This apple is hardy for zone 5. Unfortunately, in our area last 'spring' frost date is 14'th June. That happens in mountains.
I just checked the tree. It is firmly anchored, I cannot move it when I pull on it, but I found the gophers tunnels around the basked made from chicken wire. I made that basket before putting the tree inside the ground, to protect the roots. There are no detectable tunnels inside the basket (I did not dig, but used a metal pole and stick it around to test the amount of the resistance of the ground.
What do you think? Do I need to dig the roots out to see is there a damage? And can I save it? All leaves are in the same condition. There is maybe 3-4 leaves that do not show signs of the drying (The ones that are still tiny, and barely opened.)

Just leave it be and see what grows back. Cut off the dead parts when you're sure what's dead and what isn't. It will be tough making fruit under your conditions.

If you have daily freezes then the leaves on others would fry also. Most likely something else, has nothing to do with zone hardiness, let it be and see as fruitnut suggested.

One other thing came to mind, you might have purchased a diseased tree with fire blight,..leafs does look like it. You should have warranty for a year,...better to plant trees in the spring, especially for colder region like yours.

Thanks for the tip. I'll make it so.
Yes, you're right. It is touch and go with fruit, basically depends on spring conditions. Last year it was perfect for apples so there was huge amount of fruit all in the area, but year before, noting.