More likely Mediterranean Cypress Cupressus sempervirens.

It could be disease rather than just lack of water, but it isn't possible to tell from this photo. Read up on coryneum canker, caused by the fungus Seiridium cardinale; Mediterranean Cypress is moderately susceptible to this.

Resin

Or possibly you are seeing large numbers of small greenish-gray cones that will be maturing in the next few months.
I agree it is Mediterranean or Italian cypress. This species is very drought tolerant and if there was a water problem you would see brownish or reddish foliage, not gray.

Thank you for identifying my tree and giving suggestions!

I looked closely today, and I think I have spider mites because there is visible webbing on a top of the tree. I'll bring my big camera next time & will take a nice close up photo to make sure that I got it right.
I read that mites especially go for water-stressed cypress, which is exactly our case :(
For people who may have a similar problem in the future, here is the way to get rid of mites:

"If a treatment for mites is necessary, use selective materials, preferably insecticidal soap or insecticidal oil. Petroleum-based horticultural oils or neem oils are both acceptable. Do not use soaps or oils on water-stressed plants or when temperatures exceed 90°F. These materials may be phytotoxic to some plants, so check labels and/or test them out on a portion of the foliage several days before applying a full treatment. Oils and soaps must contact mites to kill them so excellent coverage, especially on the undersides of leaves, is essential and repeat applications may be required. Sulfur dust or spray can be used on some vegetables, but will burn cucurbits. Do not use sulfur dust if temperatures exceed 90°F and do not apply sulfur within 30 days of an oil spray. Sulfur dusts are skin irritants and eye and respiratory hazards. Always wear appropriate protective clothing."

Also, there is a good article on them here: http://www.evergreengardenworks.com/mites.htm

Spider mites don't make webs. They are so small that tapping the limbs with a sheet of white paper under the limb will bring them off for positive identification.

Dave

Dave,

I don't know anything about gardening, so all info I got was from several web sites.

This one says:
Many spider mites produce webbing, particularly when they occur in high populations. This webbing gives the mites and their eggs some protection from natural enemies and environmental fluctuations. Webbing produced by spiders, as well as fluff produced by cottonwoods, often is confused with the webbing of spider mites.

This one:
Spruce Mite. This serious pest is found only on conifers, hemlock, arborvitae, spruce, fir, juniper, and, occasionally, pine. A fine webbing, which collects dust and dirt, is produced on the foliage where it feeds. Infested plants lose their color and the foliage becomes thin, because severely damaged needles drop prematurely...
When mites are numerous, fine webbing is often visible...

If you google spider mites webbing, you will see many articles mentioning that web-spinning mites exist.

"When mites are numerous, fine webbing is often visible"...

I would think if the damage has progressed that far it's to late for the plant and the damage is irreversible I have never seen spider mite webs on my plants in the Midwest.

When I have found spider mites on my plants a heavy spray with the garden hose several times usually removed them from the host plant. I dislike chemical applications for environmental reasons. Sometimes you have no recourse depending on what is killing your plants but spider mites are easier controlled with plain old hose and water if indeed that is your problem. Get the white paper out and go bang on a limb. If nothing is crawling there invite you county extension agent out to have a look or take a limb to him for evaluation. It's best to know what you are treating.

Dave

I have high quality photos to show you what's going on with this plant.
{{gwi:668833}}
{{gwi:668829}}
This is how the border between green & gray looks like:
{{gwi:668836}}
bigger photo{{gwi:668831}}

I went to a local nursery, showed them one of the photos and they told me that I had mites problem, which is very common here, according to them.

They said that they spray their cypress trees every week and gave me some 55% solution, which I have to spray (1 teaspoon per gallon of water) directly on trees. I don't remember the name of it. I'll post it later, when I'm at home.