I would contend that we tend to overestimate the effectiveness of bows vs armour, and that the armour would likely prevent at least some percentage of the damage to the mount.
If we look at the wiki article on Barding we find the following (emphasis mine):
During the Late Middle Ages as armour protection for knights became
more effective, their mounts became targets. This vulnerability was
exploited by the Scots at the Battle of Bannockburn in the 14th
century, when horses were killed by the infantry, and for the English
at the Battle of Crécy in the same century where longbowmen shot
horses and the then dismounted French knights were killed by heavy
infantry. Barding developed as a response to such events.
So why would you develop and build something, unless it worked?
I have watched a video, ARROWS vs ARMOUR - Medieval Myth Busting
, showing a bit of experimental archaeology which investigates the issue of bows vs armour. Though I would normally cringe to use a YouTube video as a source, I feel this one is extremely well done, has measured the physics involved, goes to lengths to try to simulate period weapons and armours, and Tobias Capwell, curator of Arms and Armour at the Wallace Collection in London is present to oversee the process.
This above-mentioned video, though it is concerning human armour and not horse barding, does use energies and armour thicknesses which fall into the range you mention, so the physics should be similar. The archer is shooting 160lb, 80g arrows, which are developing 123J of energy at 10m, and down to 109J (about 80 ft-lbs) at the testing range of 25m. Similar to the (unsourced) energy from the OP's question.
The armour being shot at, in order to simulate examined museum specimens, varies from 1.5mm to 2.5mm in thickness. Again similar range to the numbers quoted in the question.
Information we can draw from the video is that arrows which hit head on may dent, but not penetrate (very reminiscent as to how modern body armor works). Most arrows break, and any that hit slightly obliquely, or in the more curved regions, ricochet away. This deflection may be of primary importance with a horse, keeping raking shots which might tear at the animals flanks from doing any damage, and deflecting away at least a percentage of the shots finding a target.
Note that one of only three complete sets of equestrian armour is found in the same above mentioned Wallace Collection, a beautiful set of German armor, dated to about 1480:
We can draw some information from the Wallace Collection exhibit as well. In looking at the information from the exhibit we find weights listed concerning the armor:
27.161kg (man's armour); 30.07kg (horse's armour); 10.17kg (mail)
(About 150lbs) From this we can see that the plate mail barding was expected to be worn in conjunction with chainmail protection as well. The chainmail can deal with slashing damage when engaged close-up. We can also observe the plate portion of the barding was mainly applied in curving sweeps along the breast, the top of the neck, and the upper region of the horses hind quarters. These are exactly the regions you might expect to receive fire from, during either an overhead barrage of arrows, or directly from the front during a charge. One more note concerning the Wallace Collection armour, comes from the description on this page where it defines this armor as
‘field’ armour (i.e. armour for war)
This set of armor was field armour, it was made for war, not for parades or tournaments.
So in conclusion, if we can compare the bit of experimental archaeology can be applied to your barding question, it would seem that barding would provide at least some protection from archers. The curved metal surfaces would deflect many indirect strikes, decreasing the amount of damage possibly taken by the horse. The physics tested out in the video indicate the possibility that even direct shots might not have been able to penetrate, further reducing the chance of the horse being brought down. Every arrow deflected or stopped increased your odds off reaching the battle. Statistically it increased the number of knights delivered to the fight.
That was the point of horse armour. Increased survivability.