Those look like a some kind of arborvitae. They can be trimmed back, but not too far at once. If you part the branches you'll see the greenery is only on the outside of the bush, the inside is bare branches. You can not trim back to the bare branches, they can not sprout fresh foliage there.

I just had to cut down some giant arborvitae at the house we moved into. They had been allowed to grow way too large for the space where they were planted and trimming them back to the needed space would have eliminated nearly all the greenery.

I hated to do it, I helped plant them about 25 years ago, but they were rubbing on the roof and eaves (a bigger variety then you have here) and from on the porch you were just looking into the bare branch interior of the bush.