How effective was it? what types of barding were used?

Ben,

What era? What location? Barding has been made of the same materials and in basically the same manner as the riders armour in nearly every cavalry using culture at one time or another. To restrict it to Europe there are tons of period illustrations showing bards. As an example, the Luttrell Psalter (1325-1340) shows a caparisoned horse armoured with only a shaffron, other illustrations show mail under the caparison. Various household accounts include orders for bards "made in the manner of a brigantine" and others of quilted fabric. Cuir bouilli examples exist in various collections. At the other extreme are the full plate bards made after 1450, several are shown in "The Armored Horse in Europe, 1480-1620". There were also specialized bards for the joust, popular in "Germany" these were basically giant pads to prevent injury to the horse through a collision in the course of the contest.

The effectiveness of horse armour is not something I have made a study of and I haven't come across any hard information. There are anecdotes about men-at-arms riding through a pike square without being injured, not having reason to doubt these, the horse would have to be as well armoured as the man. I would infer due to the investment required and the massive expense of good horses that it was effective, or at least effective enough.

How vulnerable horse in a close fighting that lasts some time actually is? Would infantryman automatically strike horse when horseman appeared in front of him or there is no time to waste on horse while man on the horse attacks you? I don't think horse charge on spearmen, of course spearmen would try to stop the charge with meeting the horses with spears. And what about cavalry vs cavalry fight? Would cavalrymen try to kill the opponents horses as soon as possible or concentrate on the real enemy?

Nobody can answer your question in an online forum. You need to at least make an effort to do your own research and ask questions later, not vice versa. Pick a specific time period. Pick a specific region or culture. Then ask a specific question AFTER you have used the search function and tried to find the answer elsewhere.

The various components can be found online or in a great many armour books. Don't be lazy.

Caparison: A flexible armored blanket (quilted cloth, scale, or mail) covering the animal’s back, chest, and hindquarters, reaching down to the knees or even lower. Also known as a "trapper", it sometimes had a hole for the saddle.
Chanfron: Head armor.
Crinet: Protects the back and sides of the animal’s neck.
Peytral: A rigid plate protecting the chest.
Crupper: Plate armor protecting the animal’s hindquarters and upper legs
Flanchards: Plate armor attached to the saddle covering the flanks of the animal. It closed the gap between crupper and peytral.

I would like to see some images of European horse armor from 1100 - 1450 AD.

J