I would like to believe that there are much more than 1000 reindeer in Norway. However, if there aren't, then the death of 323 reindeer will greatly affect the hunting season. Even if there were much more reindeer, there's a probability that many of them might have been scared away by the lightning. This will also hurt the season.
The mass death of reindeer should affect the hunting season. Limits on legal kills should be adjusted to maintain a healthy population next season. Care must be taken to avoid significant losses. The population will rebuild naturally as long as balance is kept, and Norway needs to consider how this affects them long-term.
In an area as small as Norway, 323 missing reindeer is a sizable amount. The early hunters probably won't be affected as much, but later in the hunting season the supply will probably have considerably dried up. This also has the potential to affect future hunting seasons as well, as those reindeer aren't around to have further generations.
No, reindeer do not roam freely like deer or elk, but are kept in herds by owners. The reindeer are allowed to graze, similar to free-roaming cattle being herded by cowboys in the old West. Each animal is carefully marked and tracked. While the owner surely suffered a big economic setback from the lightning, it will not affect hunting.