Catching a prey is not easy for wolves, even if they hunt in a group. A healthy deer runs faster than wolves. When a pack of wolves' attack moose and bison, they huddle together and do not let the wolves come close. Eventually, the wolves get frustrated and give up. It has been shown in some studies that when wolves hunt deer, out of 100, on an average 84 to 87 percent manage to escape. They usually manage to catch deer which are very young, old or sick.
You might have seen hunting wolves growling and snarling on TV channels like animal planet or discovery. It is an expression of an intention to fight. They do not growl or snarl at their prey but at each other when get into a brawl because of that prey. In fact, when they hunt they become excited, happy and even friendly. When they stare at their prey, their tails wag; ears are up and look quite focused.
When wolves manage to catch a prey, they usually eat up to 20% of their body mass. The reason they stuff themselves so much is that it's not every day they get the chance to eat fresh meat. Wolves live in harmony with each other because they have to hunt in a group.
Alpha wolf is the highest ranking wolf. He generally eats first but when a wolf from a lower rank is hungrier, then it gets to eat the fresh meat. At times, a low ranking wolf has to defend the food until a high ranking wolf is done eating. Omega wolf has the lowest rank in wolves that generally lives on the fringes of the pack. He usually eats food last.
However, wolf pups, who are too old to nurse and too little to hunt, are fed by their mothers. But in later stages, they start begging the adults for flesh. In the end, adult wolves have to throw up the food which is in their stomach and then the puppies eat the regurgitated food.