Surgery began at 1pm - almost over now, according to ESPN. Quote from the surgeon, before the operation began -

"You do not see this severe injury frequently because the fact is most horses that suffer this typically are put down on the race track," said Richardson, the chief of surgery for the center. "This is rare."
Barbaro will be taken to a Recovery Pool until he is completely awake - then to a padded stall.

I pray he will be able to tolerate the situation better than Ruffian did.